1

JEE Advanced 2022 Paper 2 Online

Numerical

+3

-1

Consider the hyperbola

$$ \frac{x^{2}}{100}-\frac{y^{2}}{64}=1 $$

with foci at $S$ and $S_{1}$, where $S$ lies on the positive $x$-axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $\angle S P S_{1}=\alpha$, with $\alpha<\frac{\pi}{2}$. The straight line passing through the point $S$ and having the same slope as that of the tangent at $P$ to the hyperbola, intersects the straight line $S_{1} P$ at $P_{1}$. Let $\delta$ be the distance of $P$ from the straight line $S P_{1}$, and $\beta=S_{1} P$. Then the greatest integer less than or equal to $\frac{\beta \delta}{9} \sin \frac{\alpha}{2}$ is ________.

$$ \frac{x^{2}}{100}-\frac{y^{2}}{64}=1 $$

with foci at $S$ and $S_{1}$, where $S$ lies on the positive $x$-axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $\angle S P S_{1}=\alpha$, with $\alpha<\frac{\pi}{2}$. The straight line passing through the point $S$ and having the same slope as that of the tangent at $P$ to the hyperbola, intersects the straight line $S_{1} P$ at $P_{1}$. Let $\delta$ be the distance of $P$ from the straight line $S P_{1}$, and $\beta=S_{1} P$. Then the greatest integer less than or equal to $\frac{\beta \delta}{9} \sin \frac{\alpha}{2}$ is ________.

Your input ____

2

JEE Advanced 2021 Paper 2 Online

Numerical

+4

-0

Let E be the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$. For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment joining P and Q'. Then the maximum possible value of the distance between M(P, Q) and M(P, Q'), as P, Q and Q' vary on E, is _______.

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3

JEE Advanced 2017 Paper 1 Offline

Numerical

+3

-0

For how many values of p, the circle x

^{2}+ y^{2}+ 2x + 4y $$-$$ p = 0 and the coordinate axes have exactly three common points?Your input ____

4

JEE Advanced 2015 Paper 2 Offline

Numerical

+4

-0

Suppose that the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ are $$\left( {{f_1},0} \right)$$ and $$\left( {{f_2},0} \right)$$ where $${{f_1} > 0}$$ and $${{f_2} < 0}$$. Let $${P_1}$$ and $${P_2}$$ be two parabolas with a common vertex at $$(0,0)$$ and with foci at $$\left( {{f_1},0} \right)$$ and $$\left( 2{{f_2},0} \right)$$, respectively. Let $${T_1}$$ be a tangent to $${P_1}$$ which passes through $$\left( 2{{f_2},0} \right)$$ and $${T_2}$$ be a tangent to $${P_2}$$ which passes through $$\left( {{f_1},0} \right)$$. If $${m_1}$$ is the slope of $${T_1}$$ and $${m_2}$$ is the slope of $${T_2}$$, then the value of $$\left( {{1 \over {m_1^2}} + m_2^2} \right)$$ is

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Questions Asked from Conic Sections (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2021 Paper 2 Online (1)
JEE Advanced 2017 Paper 1 Offline (1)
JEE Advanced 2015 Paper 2 Offline (1)
JEE Advanced 2015 Paper 1 Offline (2)
JEE Advanced 2013 Paper 1 Offline (1)
IIT-JEE 2012 Paper 1 Offline (1)
IIT-JEE 2011 Paper 1 Offline (1)
IIT-JEE 2010 Paper 1 Offline (1)

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