AB is a chord of the parabola y^2 = 4ax with | vedclass

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

Question

(C) Let the coordinates of point $B$ be $(x, y)$.Since $B$ lies on the parabola $y^2 = 4ax$,we have $y^2 = 4ax$.The slope of $AB$ is $m_1 = \frac{y}{x

Vedclass · Accepted Answer

$4a$

Vedclass · Answer

(C) Let the coordinates of point $B$ be $(x, y)$.Since $B$ lies on the parabola $y^2 = 4ax$,we have $y^2 = 4ax$.The slope of $AB$ is $m_1 = \frac{y}{x}$.Since $BC \perp AB$,the slope of $BC$ is $m_2 = -\frac{x}{y}$.The equation of line $BC$ passing through $(x, y)$ is $(Y - y) = -\frac{x}{y}(X - x)$.To find the point $C$ on the axis of the parabola (where $Y = 0$),we set $Y = 0$:$-y = -\frac{x}{y}(X - x) \implies y^2 = x(X - x) \implies 4ax = x(X - x) \implies 4a = X - x$.Thus,the projection of $BC$ on the axis is $DC = X - x = 4a$.

$AB$ is a chord of the parabola $y^2 = 4ax$ with one endpoint $A$ at the vertex of the parabola. $BC$ is drawn perpendicular to $AB$ and meets the axis of the parabola at $C$. What is the projection of $BC$ on the axis of the parabola?

Similar Questions

How many parabolas can be drawn if the endpoints of the latus rectum are given?

The equation of the common tangent to the circle $x^{2}+y^{2}=2$ and the parabola $y^{2}=8x$ is

Number of intersecting points of the conics $4x^{2} + 9y^{2} = 1$ and $4x^{2} + y^{2} = 4$ is

The point$(s)$ on the parabola $y^2 = 4x$ which are closest to the circle $x^2 + y^2 - 24y + 128 = 0$ is/are:

The locus of the midpoints of the chords of the hyperbola $x^{2}-y^{2}=4$,which touch the parabola $y^{2}=8x$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module