JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the tangent to the curve \(x^2+2 x-4 y+9=0\) at the point \(P (1,3)\) on it meet the \(y\)-axis at \(A\). Let the line passing through \(P\) and parallel to the line \(x -\) \(3 y=6\) meet the parabola \(y^2=4 x\) at \(B\). If \(B\) lies on the line \(2 x-3 y=8\). then \((A B)^2\) is equal to \(............\).
- A \(291\)
- B \(290\)
- C \(293\)
- D \(292\)
Answer & Solution
Correct Answer
(D) \(292\)
Step-by-step Solution
Detailed explanation
Equation of tangent at \(P(1,3)\) to the curve \(x ^2+2 x -4 y +9=0 \text { is } y - x =2\) Then the point \(A\) is \((0,2)\) Equation of line passing through \(P\) and parallel to the line \(x -3 y =6\). The possible coordinate of \(B\) are \((4,4)\) or \((16,8)\) But \((4,4)\)…
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