The equation of a circle is $$\(x^{2}+y^{2}+p x+2 y+q=0\)$$, where $$\(p\)$$ and $$\(q\)$$ are constants. Find the equation of the normal to the circle at the point $$\(A\)$$. ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . DO NOT WRITE IN THIS MARGIN ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . (ii) Find the values of $$\(p\)$$ and $$\(q\)$$. ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ . ................................................................................................................................................ .
Exam No：9709_w24_qp_12 Year：2024 Question No：8(b)
Answer:
Knowledge points:
1.3.2 interpret and use any of the forms in solving problems (Including calculations of distances, gradients, midpoints, points of intersection and use of the relationship between the gradients of parallel and perpendicular lines.)
1.3.3 understand that the equation represents the circle with centre and radius (Including use of the expanded form.)
1.3.4 use algebraic methods to solve problems involving lines and circles (Including use of elementary geometrical properties of circles, e.g. tangent perpendicular to radius, angle in a semicircle, symmetry.) (Implicit differentiation is not included.)
Solution:
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