Find the equation of the parabola with focus | vedclass

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

Question

(A) Let the vertex be $A(4, -1)$ and the focus be $S(4, -3)$.The axis of the parabola is the line passing through the focus and the vertex,which is $x

Vedclass · Accepted Answer

$x^{2} - 8x + 8y + 24 = 0$

Vedclass · Answer

(A) Let the vertex be $A(4, -1)$ and the focus be $S(4, -3)$.The axis of the parabola is the line passing through the focus and the vertex,which is $x = 4$.Since the vertex $A(4, -1)$ is at a distance $a = |-1 - (-3)| = 2$ from the focus $S(4, -3)$,and the parabola opens downwards (as the focus is below the vertex),the equation of the parabola is of the form $(x - h)^{2} = -4a(y - k)$,where $(h, k)$ is the vertex.Here,$(h, k) = (4, -1)$ and $a = 2$.Substituting these values,we get:$(x - 4)^{2} = -4(2)(y - (-1))$$(x - 4)^{2} = -8(y + 1)$$x^{2} - 8x + 16 = -8y - 8$$x^{2} - 8x + 8y + 24 = 0$.

Find the equation of the parabola with focus $(4, -3)$ and vertex $(4, -1)$.

Similar Questions

If the lines $2x + 3y + 12 = 0$ and $x - y + k = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $k$ is equal to

$A$ parabola having its axis parallel to the $Y$-axis passes through the points $(0, 2/5)$,$(4, -2)$,and $(1, 8/5)$. Which of the following points lies on this parabola?

Statement $I$: $4x^2+y^2-4xy-30x-50y+40=0$ is the equation of a parabola having $(2,3)$ as its focus and $x+2y+5=0$ as its directrix.
Statement $II$: The equation of the directrix of the parabola $x^2-4x+16y+52=0$ is $y+1=0$.
Which of the above statements is (are) true?

The vertex of the parabola $x^2 + 8x + 12y + 4 = 0$ is

The length of the chord of the parabola $y^2 = x$ which is bisected at the point $(2, 1)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module