JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(A\) be a point on the \(x\)-axis. Common tangents are drawn from \(A\) to the curves \(x^2+y^2=8\) and \(y^2= 16x.\) If one of these tangents touches the two curves at \(Q\) and \(R\), then \(( QR )^2\) is equal to
- A \(64\)
- B \(76\)
- C \(81\)
- D \(72\)
Answer & Solution
Correct Answer
(D) \(72\)
Step-by-step Solution
Detailed explanation
\(y = mx +\frac{4}{ m }\) \(\frac{\left|\frac{4}{ m }\right|}{\sqrt{1+ m ^2}}=2 \sqrt{2} \therefore m =\pm 1\) \(y=\pm x \pm 4\). Point of contact on parabola Let \(m=1,\left(\frac{a}{m^2}, \frac{2 a}{m}\right)\) \(R (4,8)\) Point of contact on circle \(Q (-2,2)\)…
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