If the tangents drawn at the points and on the parabola intersect at the point , then the orthocentr

Q: JEE Main 2021 Conic Sections: If the tangents drawn at the points and on the parabola intersect at the point , then the orthocentr...

The correct answer is A. The problem asks us to find the orthocentre of a triangle PQR, where P and Q are points on the parabola , and R is the intersection point of the tangents drawn to the parabola at P and Q. The point R is given as . To solve this, we will first identify the coordinates of P and Q, then the slopes of the sides of , and finally determine the orthocentre by finding the intersection of two altitudes. --- **1. Standardizing the Parabola Equation and Finding Key Parameters** The given parabola equation

Question

If the tangents drawn at the points and on the parabola intersect at the point , then the orthocentre of the triangle is :

Accepted Answer

The problem asks us to find the orthocentre of a triangle PQR, where P and Q are points on the parabola $y^2 = 2x-3$ , and R is the intersection point of the tangents drawn to the parabola at P and Q. The point R is given as $(0,1)$ .

To solve this, we will first identify the coordinates of P and Q, then the slopes of the sides of $\triangle PQR$ , and finally determine the orthocentre by finding the intersection of two altitudes.

1. Standardizing the Parabola Equation and Finding Key Parameters

The given parabola equation is $y^2 = 2x - 3$ . To work with it more easily, we can rewrite it in the standard form $Y

Answer

(0, 1)

Answer

(2, 1)

Answer

(6, 3)

Answer

(2, 1)

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