JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P (a, b )\) be a point on the parabola \(y ^{2}=8 x\) such that the tangent at \(P\) passes through the centre of the circle \(x ^{2}+ y ^{2}-10 x -14 y +65=0\). Let \(A\) be the product of all possible values of \(a\) and \(B\) be the product of all possible values of \(b\). Then the value of \(A + B\) is equal to.
- A \(0\)
- B \(25\)
- C \(40\)
- D \(65\)
Answer & Solution
Correct Answer
(D) \(65\)
Step-by-step Solution
Detailed explanation
\(P ( a , b )\) is point on \(y ^{2}=8 x\), such that tangent at \(P\) pass through centre of \(x ^{2}+ y ^{2}-10 x -14 y +65=0\) i.e. \((5,7)\) Tangent at \(P \left(a t ^{2}, 2 at \right)\) is ty \(= x + at ^{2}\) \(A =2\) and it pass through \((5,7)\) \(7 t =5+2 t ^{2}\)…
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