(B) Given parabola is $y^2+6y-2x+5=0$. Completing the square for $y$: $y^2+6y+9-9-2x+5=0$ $(y+3)^2-4-2x=0$ $(y+3)^2=2(x+2)$. Comparing with $(y-k)^2=4

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

(B) Given parabola is $y^2+6y-2x+5=0$. Completing the square for $y$: $y^2+6y+9-9-2x+5=0$ $(y+3)^2-4-2x=0$ $(y+3)^2=2(x+2)$. Comparing with $(y-k)^2=4a(x-h)$,we get vertex $(h, k) = (-2, -3)$. Thus,statement $I$ is true. For the directrix,$4a=2 \implies a=\frac{1}{2}$. The equation of the directrix is $x = h-a$. $x = -2 - \frac{1}{2} = -2.5$,or $2x+5=0$. Since the given directrix in statement $II$ is $y+3=0$,statement $II$ is false.

Class 11 Mathematics 10-2. Parabola, Ellipse, Hyperbola Parabola

Medium

For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?

TS EAMCET 2007 All TS EAMCET

AP EAMCET 2007 All AP EAMCET

A
Both $I$ and $II$ are true
B
$I$ is true,$II$ is false
C
$I$ is false,$II$ is true
D
Both $I$ and $II$ are false

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-2. Parabola, Ellipse, Hyperbola

Subtopic

Parabola

Previous Year

TS EAMCET 2007 Paper All TS EAMCET years →

Previous Year

AP EAMCET 2007 Paper All AP EAMCET years →

The length of the latus rectum of the parabola $9x^2 - 6x + 36y + 19 = 0$ is:

Medium

View Solution

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

MediumAP EAMCET 2006

View Solution

What is the area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola $x^2 = 8y$?

Medium

View Solution

For what value of $k$ does the line $2y - x + k = 0$ touch the parabola $x^2 + 4y = 0$?

Medium

View Solution

$A$ line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1}(\frac{3}{5})$ in the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at points $A$ and $B$, then the length $|AB|$ is equal to

EasyWBJEE 2022

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

For the parabola $y^2+6y-2x+5=0$:$(I)$ The vertex is $(-2,-3)$$(II)$ The directrix is $y+3=0$Which of the following is correct?

Similar Questions

The length of the latus rectum of the parabola $9x^2 - 6x + 36y + 19 = 0$ is:

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

What is the area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola $x^2 = 8y$?

For what value of $k$ does the line $2y - x + k = 0$ touch the parabola $x^2 + 4y = 0$?

$A$ line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1}(\frac{3}{5})$ in the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at points $A$ and $B$, then the length $|AB|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module

For the parabola $y^2+6y-2x+5=0$:
$(I)$ The vertex is $(-2,-3)$
$(II)$ The directrix is $y+3=0$
Which of the following is correct?