The length of the latus-rectum of the parabola 4 y^2+2 x-20 y+17=… - Vidyadip

MCQ

The length of the latus-rectum of the parabola $4 y^2+2 x-20 y+17=0$ is

✓
$3$
B
$6$
C
$\frac{1}{2}$
D
$9$

✓

Answer

Correct option: A.

$3$

$\frac{1}{2}$

Solution:
Given:
$4 y^2+2 x-20 y+17=0$
$\Rightarrow\ \text{y}^2+\frac{\text{x}}{2}-5\text{y}+\frac{17}{4}=0$
$\Rightarrow\ \Big(\text{y}-\frac{5}{2}\Big)^2+\frac{\text{x}}{2}-2=0$
$\Rightarrow\ \Big(\text{y}-\frac{5}{2}\Big)^2=-1\Big(\frac{\text{x}}{2}-2\Big)$
$\Rightarrow\ \Big(\text{y}-\frac{5}{2}\Big)^2=\frac{-1}{2}(\text{x}-4)$
$\text{Let }\text{X}=\text{x}-4,\ \text{Y}=\text{y}-\frac{5}{2}$
$\therefore\ \text{Y}^2=\frac{-\text{X}}{2}$
$\therefore$ Length of the latus rectum $=\ 4\text{a}=\frac{1}{2}$ units

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from CONIC SECTIONS→CONIC SECTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If in an A.P., first term is 20, common difference is 2 and nth term is 42, then find sum up to n terms.

If $\alpha,\beta$ are the roots of the equation $x^2− p(x + 1) − c = 0$, then $(\alpha+1)(\beta+1)=$

If ${\mathop{\rm Im}\nolimits} \left( {\frac{{2z + 1}}{{iz + 1}}} \right) = - 3,$ then locus of $z$ is :-

The position of the point $(8,-9)$ with respect to the lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$ is

The exact value of $\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$ is equal to

The equation of the parabola with focus (0, 0) and directrix x + y = 4 is

If $\tan\Big(\frac{\pi}{4}+\text{x}\Big)+\tan\Big(\frac{\pi}{4}-\text{x}\Big)=\lambda\sec2\text{x},$ then:

The partial fractions of ${{{x^4} + 24{x^2} + 28} \over {{{({x^2} + 1)}^3}}}$ are

If $[\text{x}^2]-5[\text{x}]+6=0,$ where [.] denotes the greatest integer function, then:

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is