1
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $P$ be a point on the parabola $y^2=4 a x$, where $a>0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $P F Q$, where $F$ is the focus of the parabola, is 120 . If the slope $m$ of the normal and $a$ are both positive integers, then the pair $(a, m)$ is
2
JEE Advanced 2022 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Consider the ellipse
$$$ \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 $$$
Let $H(\alpha, 0), 0<\alpha<2$, be a point. A straight line drawn through $H$ parallel to the $y$-axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ respectively, in the first quadrant. The tangent to the ellipse at the point $E$ intersects the positive $x$-axis at a point $G$. Suppose the straight line joining $F$ and the origin makes an angle $\phi$ with the positive $x$-axis.
List-I | List-II |
---|---|
(I) If $\phi=\frac{\pi}{4}$, then the area of the triangle $F G H$ is | (P) $\frac{(\sqrt{3}-1)^{4}}{8}$ |
(II) If $\phi=\frac{\pi}{3}$, then the area of the triangle $F G H$ is | (Q) 1 |
(III) If $\phi=\frac{\pi}{6}$, then the area of the triangle $F G H$ is | (R) $\frac{3}{4}$ |
(IV) If $\phi=\frac{\pi}{12}$, then the area of the triangle $F G H$ is | (S) $\frac{1}{2 \sqrt{3}}$ |
(T) $\frac{3 \sqrt{3}}{2}$ |
The correct option is:
3
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let a, b and $$\lambda $$ be positive real numbers. Suppose P is an end point of the latus return of the
parabola y2 = 4$$\lambda $$x, and suppose the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is
parabola y2 = 4$$\lambda $$x, and suppose the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is
4
JEE Advanced 2019 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let the circles
C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :
(i) Centre of C3 is collinear with the centres of C1 and C2.
(ii) C1 and C2 both lie inside C3 and
(iii) C3 touches C1 at M and C2 at N.
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha $$y.
There are some expression given in the List-I whose values are given in List-II below.

Which of the following is the only INCORRECT combination?
C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :
(i) Centre of C3 is collinear with the centres of C1 and C2.
(ii) C1 and C2 both lie inside C3 and
(iii) C3 touches C1 at M and C2 at N.
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha $$y.
There are some expression given in the List-I whose values are given in List-II below.

Which of the following is the only INCORRECT combination?
Questions Asked from Conic Sections (MCQ (Single Correct Answer))
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