Can you solve this JEE Advanced Question? Coordinate Geometry

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The trickiest part of coordinate geometry question! 🛑 Full solution linked in the comments!

Let 𝑃 be the point on the parabola 𝑦=𝑥2 such that the slope of the tangent to the parabola at the
point 𝑃 is 4 . Let 𝑄 be the point in the first quadrant lying on the circle 𝑥2+𝑦2=2 such that the
slope of the tangent to the circle at the point 𝑄 is −1 . Let 𝑅 be the point in the first quadrant lying
on the ellipse 𝑥2+4𝑦2=8 such that the slope of the tangent to the ellipse at the point 𝑅 is −1
2
.
Then the radius of the circle passing through the points 𝑃,𝑄 and 𝑅 is:

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Видео Can you solve this JEE Advanced Question? Coordinate Geometry канала Shaurya Agarwal