Find the coordinates of the point on the para | vedclass

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

Question

(A) The given equation of the parabola is $y^2 = 8x$. Comparing this with the standard form $y^2 = 4ax$,we get $4a = 8$,which implies $a = 2$. The foc

Vedclass · Accepted Answer

$(2, 4)$

Vedclass · Answer

(A) The given equation of the parabola is $y^2 = 8x$. Comparing this with the standard form $y^2 = 4ax$,we get $4a = 8$,which implies $a = 2$. The focal distance of a point $(x, y)$ on the parabola $y^2 = 4ax$ is given by $x + a$. Given that the focal distance is $4$,we have $x + a = 4$. Substituting $a = 2$,we get $x + 2 = 4$,so $x = 2$. Now,substitute $x = 2$ into the parabola equation $y^2 = 8x$: $y^2 = 8(2) = 16$. Therefore,$y = \pm 4$. The points are $(2, 4)$ and $(2, -4)$. Looking at the options,$(2, 4)$ is provided as option $A$.

Find the coordinates of the point on the parabola $y^2 = 8x$ whose focal distance is $4$.

Similar Questions

If a point $P$ moves such that its distances from the point $A(1, 1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is

The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^{2}$) of the triangle $PAB$ is:

Let $A$ be the focus of the parabola $y^{2}=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points $B$ and $C$. If the centroid of the triangle $ABC$ is $(\frac{7}{3},\frac{4}{3})$,then $(BC)^{2}$ is equal to:

The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(3, 2)$ is . . . .

If a parabola passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ and has a horizontal axis,then the length of the latus rectum of that parabola is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module