New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Parabola question

2025 · 23 Jan · Shift 2 · Q47

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Parabola
2025 · 23 Jan · Shift 2 · Q47

Parabola question

2025 · 23 Jan · Shift 2 · Q47

JEE MainMathematicsParabolaNumerical+4 / −1

The focus of the parabola

y^2=4 x+16

is the centre of the circle

C

of radius 5 . If the values of

\lambda

, for which C passes through the point of intersection of the lines

3 x-y=0

and

x+\lambda y=4

, are

\lambda_1

and

\lambda_2, \lambda_1\lt \lambda_2

, then

12 \lambda_1+29 \lambda_2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Parabola

If the equation of the parabola with vertex $V (\frac{3}{2}, 3)$ and the directrix $x + 2 y = 0$ is $α x^{2} + β y^{2} - γ x y - 30 x - 60 y + 225 = 0$ , then $α + β + γ$ is equal to :2025 · MCQ
Let ABCD be a trapezium whose vertices lie on the parabola $y^{2} = 4 x$ . Let the sides AD and BC of the trapezium be parallel to $y$ -axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point…2025 · MCQ
Let $A$ and $B$ be the two points of intersection of the line $y + 5 = 0$ and the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $d$ denotes the distance between $A$ and $B$ , and a denotes the area of $△ S A B$ …2025 · Numerical
Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)2 is equal to :2025 · MCQ
Let $y^{2} = 12 x$ be the parabola and $(S P) (S Q) = \frac{147}{4}$ be its focus. Let $P Q$ be a focal chord of the parabola such that $(S P) (S Q) = \frac{147}{4}$ . Let $C$ be the circle described taking $64 x^{2} + 64 y^{2} - α x - 643 y = β$ as a diameter. If the equation of a circle $C$ is $64 x^{2} + 64 y^{2} - α x - 643 y = β$ …2025 · Numerical
Let the line $L : 2 x + y = α$ pass through the point of the intersection $P$ (in the first quadrant) of the circle $x^{2} + y^{2} = 3$ and the parabola $x^{2} = 2 y$ . Let the line $L$ touch two circles $C_{1}$ …2024 · Numerical
Let the length of the focal chord PQ of the parabola $y^{2} = 12 x$ be 15 units. If the distance of $PQ$ from the origin is $p$ , then $10 p^{2}$ is equal to .2024 · Numerical
Let $P Q$ be a chord of the parabola $y^{2} = 12 x$ and the midpoint of $P Q$ be at $P$ . Then, which of the following point lies on the line passing through the points $P$ and $Q$ ?2024 · MCQ