TS EAMCET · Maths · Parabola
Let \(P(2,4), Q(18,-12)\) be the points on the parabola \(y^2=8 x\). The equation of straight line having slope \(\frac{1}{2}\) and passing through the point of intersection of the tangents to the parabola drawn at the points \(P\) and \(Q\) is
- A \(2 x-y=1\)
- B \(2 x-y=2\)
- C \(x-2 y=1\)
- D \(x-2 y=2\)
Answer & Solution
Correct Answer
(D) \(x-2 y=2\)
Step-by-step Solution
Detailed explanation
We have, equation of parabola \[ y^2=8 x \] Differentiate w.r.t. ' \(x\) ' \[ 2 y \frac{d y}{d x}=8 \quad \Rightarrow \quad \frac{d y}{d x}=\frac{4}{y} \] At point \(P(2,4)\) slope of tangent \[ m_1=\frac{4}{4}=1 \] So, equation of lst tangent…
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