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

(A) For the parabola $y^2 = 4ax$,we have $4a = 2/3$,which implies $a = 1/6$. Given the system of parallel chords $y + 2x + 1 = 0$,the slope $m$ of the

Vedclass · Accepted Answer

$y = -1/6$

Vedclass · Answer

(A) For the parabola $y^2 = 4ax$,we have $4a = 2/3$,which implies $a = 1/6$. Given the system of parallel chords $y + 2x + 1 = 0$,the slope $m$ of these chords is $-2$. The equation of the diameter corresponding to a system of parallel chords with slope $m$ for the parabola $y^2 = 4ax$ is given by $y = \frac{2a}{m}$. Substituting the values $a = 1/6$ and $m = -2$: $y = \frac{2(1/6)}{-2} = \frac{1/3}{-2} = -1/6$. Thus,the equation of the diameter is $y = -1/6$.

If the equation of a system of parallel chords of the parabola $y^2 = \frac{2}{3}x$ is $y + 2x + 1 = 0$,find its diameter.

Similar Questions

The normals at three points $P, Q, R$ of the parabola $y^2 = 4ax$ meet in $(h, k).$ The centroid of triangle $PQR$ lies on :

Find the equation of the parabola whose axis is parallel to the $y$-axis and which passes through the points $(0,4), (1,9)$ and $(4,5)$.

Consider the parabola $y^{2}=4x$. Let $P$ and $Q$ be points on the parabola where $P(4, -4)$ and $Q(9, 6)$. Let $R$ be a point on the arc of the parabola between $P$ and $Q$. Then, the area of $\Delta PQR$ is largest when

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are

If $y=mx+1$ is a tangent to the parabola $y^2=4x$,then $m=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module