What is the length of the chord intercepted b | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To find the length of the chord,we first find the points of intersection of the parabola $y = x^2 + 3x$ and the line $y = 5 - x$.Equating the two

Vedclass · Accepted Answer

$6\sqrt{2}$

Vedclass · Answer

(A) To find the length of the chord,we first find the points of intersection of the parabola $y = x^2 + 3x$ and the line $y = 5 - x$.Equating the two expressions for $y$:$x^2 + 3x = 5 - x$$x^2 + 4x - 5 = 0$$(x + 5)(x - 1) = 0$So,$x = 1$ and $x = -5$.For $x = 1$,$y = 5 - 1 = 4$. Point is $(1, 4)$.For $x = -5$,$y = 5 - (-5) = 10$. Point is $(-5, 10)$.The length of the chord is the distance between $(1, 4)$ and $(-5, 10)$:$L = \sqrt{(-5 - 1)^2 + (10 - 4)^2}$$L = \sqrt{(-6)^2 + (6)^2}$$L = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2}$.

What is the length of the chord intercepted by the parabola $y = x^2 + 3x$ on the line $x + y = 5$?

Similar Questions

The line among the following which touches the parabola $y^2=4ax$ is

Find the equation of the parabola with vertex $(-3, 0)$ and directrix $x + 5 = 0$.

$y = 3x - 2$ is a straight line touching the parabola $(y - 3)^2 = 12(x - 2)$. If a line drawn perpendicular to this line at point $P$ on it touches the given parabola,then the point $P$ is:

If $x + by + c = 0$ is a normal to the parabola $y^2 = 12x$,then the complete set of all values of $c$ is -

The two parabolas $y^2 = 4x$ and $x^2 = 4y$ intersect at a point $P$,whose abscissa is not zero,such that

Vedclass Test Series

Exam Paper Generator

Online Exam Module