JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(x^{2}+y^{2}+A x+B y+C=0\) be a circle passing through \((0,6)\) and touching the parabola \(y = x ^{2}\) at \((2,4)\). Then \(A + C\) is equal to
- A \(16\)
- B \(88 / 5\)
- C \(72\)
- D \(-8\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\(x ^{2}+ y ^{2}+ Ax + By + C =0\) is passing through \((0,6)\) \(\Rightarrow 6 B + C =-36\) The tangent of the parabola \(y = x ^{2}\) at \((2,4)\) is \(4 x - y -4=0 \quad-(1)\) The tangent of circle \(x ^{2}+ y ^{2}+ Ax + By + C =0\) at \((2,4)\) is…
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