Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S.
The radius of the circumcircle of the triangle PRS is
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S.
The radius of the incircle of the triangle PQR is
$$ \text { Normals are drawn at points } \mathrm{P}, \mathrm{Q} \text { and } \mathrm{R} \text { lying on the parabola } y^2=4 x \text { which intersect at }(3,0) \text {. Then } $$
| (i) | Area of $\triangle \mathrm{PQR}$ | (A) | 2 |
|---|---|---|---|
| (ii) | Radius of circumcircle of $\triangle \mathrm{PQR}$ | (B) | 5/2 |
| (iii) | Centroid of $\triangle \mathrm{PQR}$ | (C) | (5/2,0) |
| (iv) | Circumcentre of $\triangle \mathrm{PQR}$ | (D) | (2/3,0) |
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