AP EAMCET · Maths · Parabola
If the tangents of the parabola \(y^2=8 x\) passing through the point \(P(1,3)\) touches the parabola at \(A\) and \(B\), then the area (in sq. units) of \(\triangle A B C\) is
- A \(1\)
- B \(\frac{3}{4}\)
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(y^2 = 8x \implies 4a = 8 \implies a = 2\) \(P(x_1, y_1) = (1,3)\) \text{Area of } \triangle ABC = \frac{1}{2a} |y_1^2 - 4ax_1|^{3/2}\) \text{Area} = \frac{1}{2(2)} |3^2 - 4(2)(1)|^{3/2}\) \text{Area} = \frac{1}{4} |9 - 8|^{3/2}\) \text{Area} = \frac{1}{4} |1|^{3/2}\)…
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