The length of the latus rectum of 3x^{2} - 4y | vedclass

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

Question

(B) Given equation of the conic is $3x^{2} - 4y + 6x - 3 = 0$. Rearranging the terms,we get $3x^{2} + 6x = 4y + 3$. Taking $3$ as a common factor,$3(x

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(B) Given equation of the conic is $3x^{2} - 4y + 6x - 3 = 0$. Rearranging the terms,we get $3x^{2} + 6x = 4y + 3$. Taking $3$ as a common factor,$3(x^{2} + 2x) = 4y + 3$. Completing the square inside the bracket,$3(x^{2} + 2x + 1 - 1) = 4y + 3$. $3((x + 1)^{2} - 1) = 4y + 3$. $3(x + 1)^{2} - 3 = 4y + 3$. $3(x + 1)^{2} = 4y + 6$. $(x + 1)^{2} = \frac{4}{3}(y + \frac{6}{4}) = \frac{4}{3}(y + \frac{3}{2})$. Comparing this with the standard form of a parabola $X^{2} = 4aY$,where $X = x + 1$ and $Y = y + \frac{3}{2}$,we have $4a = \frac{4}{3}$. The length of the latus rectum is $4a = \frac{4}{3}$.

The length of the latus rectum of $3x^{2} - 4y + 6x - 3 = 0$ is

Similar Questions

For the parabola $y^2 = 4ax$,what is the $x$-coordinate of the point closest to the focus?

If a normal chord of a parabola $y^2 = 4ax$ subtends a right angle at the origin,then the slope of that normal chord is

The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is

If the normal at the point $t_1$ (i.e.,at $(at_1^2, 2at_1)$) on the parabola $y^2 = 4ax$ meets the parabola again at the point $t_2$,then $t_1t_2$ is equal to:

The locus of a point such that two tangents drawn from it to the parabola $y^2 = 4ax$ are such that the slope of one is double the other is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module