1
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
Out of Syllabus
Let $\mathrm{S}$ be the set of all $\mathrm{a} \in \mathrm{N}$ such that the area of the triangle formed by the tangent at the point $\mathrm{P}(\mathrm{b}$, c), b, c $\in \mathbb{N}$, on the parabola $y^{2}=2 \mathrm{a} x$ and the lines $x=\mathrm{b}, y=0$ is $16$ unit2, then $\sum\limits_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to :
2
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Out of Syllabus

A triangle is formed by the tangents at the point (2, 2) on the curves $$y^2=2x$$ and $$x^2+y^2=4x$$, and the line $$x+y+2=0$$. If $$r$$ is the radius of its circumcircle, then $$r^2$$ is equal to ___________.

3
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1
Out of Syllabus

Two tangent lines $$l_{1}$$ and $$l_{2}$$ are drawn from the point $$(2,0)$$ to the parabola $$2 \mathrm{y}^{2}=-x$$. If the lines $$l_{1}$$ and $$l_{2}$$ are also tangent to the circle $$(x-5)^{2}+y^{2}=r$$, then 17r is equal to ___________.

4
JEE Main 2022 (Online) 25th July Morning Shift
Numerical
+4
-1
Out of Syllabus

The sum of diameters of the circles that touch (i) the parabola $$75 x^{2}=64(5 y-3)$$ at the point $$\left(\frac{8}{5}, \frac{6}{5}\right)$$ and (ii) the $$y$$-axis, is equal to ______________.