Question:
The focus of the parabola \( (y + 1)^2 = -8(x + 2) \) is
The focus of the parabola \( (y + 1)^2 = -8(x + 2) \) is
Show Hint
Negative \( a \) indicates parabola opens left.
Updated On: May 1, 2026
- \( (-4,-1) \)
- \( (-1,-4) \)
- \( (1,4) \)
- \( (4,1) \)
- \( (-1,4) \)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
Standard form:
\[
(y-k)^2 = 4a(x-h)
\]
Focus:
\[
(h+a, k)
\]
Step 1: Compare with standard form.
\[ (y+1)^2 = -8(x+2) \] So: \[ h = -2,\quad k = -1,\quad 4a = -8 \Rightarrow a = -2 \]
Step 2: Find focus.
\[ (h+a, k) = (-2 -2, -1) = (-4, -1) \]
Step 1: Compare with standard form.
\[ (y+1)^2 = -8(x+2) \] So: \[ h = -2,\quad k = -1,\quad 4a = -8 \Rightarrow a = -2 \]
Step 2: Find focus.
\[ (h+a, k) = (-2 -2, -1) = (-4, -1) \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM sections of a cone Questions
- Given that: \[ \frac{1}{\tan A - \tan B} = \]
- cos \( A \cos 2A \) is equal to:
- If \( y = \frac{1 + \tan^2 x}{1 - \tan^2 x} \), find \( y' \left( \frac{\pi}{8} \right) \), where \( 0<x<\frac{\pi}{4} \).
- The axis of the parabola \(x^{2} + 6x + 4y + 5 = 0\) is
- The distance between the foci of the ellipse \(\frac{(x + 2)^{2{9} + \frac{(y - 1)^{2}}{4} = 1\) is}
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions