TS EAMCET · Maths · Parabola
If \(y=m x+c\) is a common tangent to the parabola \(y^2=4 \sqrt{k} x\) and the circle \(2 x^2+2 y^2=k\) then the product of the slopes of such common tangents is
- A \(-2\)
- B \(\frac{k+2}{3}\)
- C \(-1\)
- D \(\frac{k}{2}\)
Answer & Solution
Correct Answer
(C) \(-1\)
Step-by-step Solution
Detailed explanation
The equation of a tangent to \(y^2=4 \sqrt{k} x\) is \(y=m x+\sqrt{k} / m\), where \(m\) is the slope of tangent. If it touches the \(2 x^2+2 y^2=k\), then…
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