The distance between the points (am_1^2, 2am_ | vedclass

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

Question

(A) The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Substituting the given po

Vedclass · Accepted Answer

$a(m_1 - m_2)\sqrt{(m_1 + m_2)^2 + 4}$

Vedclass · Answer

(A) The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Substituting the given points $(am_1^2, 2am_1)$ and $(am_2^2, 2am_2)$:$d = \sqrt{(am_2^2 - am_1^2)^2 + (2am_2 - 2am_1)^2}$$d = \sqrt{a^2(m_2^2 - m_1^2)^2 + 4a^2(m_2 - m_1)^2}$$d = \sqrt{a^2(m_2 - m_1)^2(m_2 + m_1)^2 + 4a^2(m_2 - m_1)^2}$$d = \sqrt{a^2(m_2 - m_1)^2 [(m_1 + m_2)^2 + 4]}$$d = a|m_1 - m_2|\sqrt{(m_1 + m_2)^2 + 4}$.

The distance between the points $(am_1^2, 2am_1)$ and $(am_2^2, 2am_2)$ is

Similar Questions

Let $A$ be the vertex and $L$ be the length of the latus rectum of the parabola $y^2 - 2y - 4x - 7 = 0$. Find the equation of the parabola with $A$ as the vertex,$2L$ as the length of the latus rectum,and the axis at right angles to that of the given curve.

The axis of a parabola lies along the $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin on the positive $x$-axis,then which of the following points does not lie on it?

If the normals at two points on the parabola $y^2 = 4ax$ meet on the parabola,then what is the product of the ordinates of these two points?

If $(2, -8)$ is one endpoint of a focal chord of the parabola $y^{2} = 32x$,what is the other endpoint?

The equation of a straight line drawn through the focus of the parabola $y^2 = -4x$ at an angle of $120^\circ$ to the $x$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module