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

Both

I

and

I I

are correct

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I

is true,

I I

is false

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Both

I

and

I I

are false

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I

is false,

I I

is true

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Solution

The correct option is B Both $I$ and $I I$ are false
The general equation of a parabola has form $a y^{2} + b y + c = x$ or $x - h = p (y - k)^{2}$ .
The vertex lies at $y = - \frac{b}{2 a} = - 3 ⟹ x = - 7$
hence, vertex of parabola is at $(- 7, - 3)$
Hence, the directrix is $x + h + a = 0 = - 7 - \frac{1}{2} = - 7.5$
Both I and II are false.

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Similar questions

For the parabola $y^{2} + 6 y - 2 x + 5 = 0$ (i) The vertex is $(- 2, - 3)$ (ii) The directrix is $y + 3 = 0$ which of the following is correct?

Observe the following statements

$(i) I n Δ A B C, b c o s^{2} \frac{C}{2} + c c o s^{2} \frac{B}{2} = s$

$(i i) I n Δ A B C, c o t \frac{A}{2} = \frac{b + c}{a} \Rightarrow B = 90^{0}$

Which of the following is correct?

Q. Let A be a

2 \times 2

matrix
Statement - I : adj (adj A) = A
Statement - II : |adj A| = |A|

Question 29

In a pair of adjacent angles, (i) vertex is always common (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. then
(a) all (i), (ii) and (iii) are true
(b) (iii) is false
(c) (i) is false but (ii) and (iii) are true
(d) (ii) is false

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Statement - II: Isoelectronic species should have same charges.

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For the parabola y2+6y−2x=5(I) The vertex is (−2,−3)(II) The directrix is y+3=0Which of the following is correct?

The correct option is B Both I and II are falseThe general equation of a parabola has form ay2+by+c=x or x−h=p(y−k)2.The vertex lies at y=−b2a=−3⟹x=−7 hence, vertex of parabola is at (−7,−3)Hence, the directrix is x+h+a=0=−7−12=−7.5Both I and II are false.

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