The point $$\(A\)$$ has coordinates $$\((1,5)\)$$ and the line $$\(l\)$$ has gradient $$\(-\frac{2}{3}\)$$ and passes through $$\(A\)$$. A circle has centre $$\((5,11)\)$$ and radius $$\(\sqrt{52}\)$$. Find the equation of the other circle of radius $$\(\sqrt{52}\)$$ for which $$\(l\)$$ is also the tangent at $$\(A\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s21_qp_12 Year：2021 Question No：7(b)
Answer:
Centre is \((-3,-1)\)
Equation is \((x+3)^{2}+(y+1)^{2}=52\)
Equation is \((x+3)^{2}+(y+1)^{2}=52\)
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.)
Solution:
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