If the tangent at a point π on the parabola \(π¦^2=3π₯\) is parallel to the line \(π₯+2π¦=1\) and the tangents at the points π and π
on the ellipse \(\frac{π₯^2}{ 4} +\frac{π¦^2}{ 1} =1\) are perpendicular to the line π₯βπ¦=2, then the area of the triangle PQR is :
- \(\frac{3}{2}\sqrt 5\)
- \(5\sqrt 3\)
- \(3\sqrt 5\)
- \(\frac{9}{\sqrt 5}\)
The Correct Option is C
Solution and Explanation
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Concepts Used:
Conic Sections
When a plane intersects a cone in multiple sections, several types of curves are obtained. These curves can be a circle, an ellipse, a parabola, and a hyperbola. When a plane cuts the cone other than the vertex then the following situations may occur:
Let βΞ²β is the angle made by the plane with the vertical axis of the cone
- When Ξ² = 90Β°, we say the section is a circle
- When Ξ± < Ξ² < 90Β°, then the section is an ellipse
- When Ξ± = Ξ²; then the section is said to as a parabola
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