If the equation of a system of parallel chord | vedclass

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

Question

(D) The equation of the parabola is $y^2 = \frac{25}{7}x$. Comparing this with $y^2 = 4ax$,we get $4a = \frac{25}{7}$,so $a = \frac{25}{28}$.Given the

Vedclass · Accepted Answer

$56y = 25$

Vedclass · Answer

(D) The equation of the parabola is $y^2 = \frac{25}{7}x$. Comparing this with $y^2 = 4ax$,we get $4a = \frac{25}{7}$,so $a = \frac{25}{28}$.Given the system of parallel chords is $4x - y + \lambda = 0$,the slope of these chords is $m = 4$.The equation of the diameter of a parabola $y^2 = 4ax$ corresponding to chords of slope $m$ is given by $y = \frac{2a}{m}$.Substituting the values,$y = \frac{2 	imes (25/28)}{4} = \frac{50/28}{4} = \frac{50}{112} = \frac{25}{56}$.Thus,$56y = 25$.

If the equation of a system of parallel chords of the parabola $y^2 = \frac{25x}{7}$ is $4x - y + \lambda = 0$,then the equation of the corresponding diameter is . . . . . .

Similar Questions

The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

At which point does the line $x = my + \frac{a}{m}$ touch the parabola $x^2 = 4ay$?

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

$A$ set of parallel chords of the parabola $y^2 = 4ax$ have their mid-points on:

From an external point $P(h, k)$,a pair of tangent lines are drawn to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the inclinations of these tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,then the locus of $P$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module