JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(y = m _{1} x + c _{1}\) and \(y = m _{2} x + c _{2}, m _{1} \neq m _{2}\) are two common tangents of circle \(x^{2}+y^{2}=2\) and parabola \(y^{2}=x\), then the value of \(8\left|m_{1} m_{2}\right|\) is equal to
- A \(3+4 \sqrt{2}\)
- B \(-5+6 \sqrt{2}\)
- C \(-4+3 \sqrt{2}\)
- D \(7+6 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(-4+3 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(C_{1}: x^{2}+y^{2}=2\) \(C_{2}: y^{2}=x\) Let tangent to parabola be \(y = mx +\frac{1}{4 m }\). It is also a tangent of circle so distance from centre of circle \((0,0)\) will be \(\sqrt{2}\).…
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