Question:medium

The distance of the point $(1,2)$ from the directrix of the parabola \[ y^2-4x-4y+8=0 \] is:

Show Hint

For the parabola \[ (y-k)^2=4a(x-h), \] remember: \[ \text{Focus}=(h+a,k), \] \[ \text{Directrix}=x=h-a. \] Once the directrix is known, finding the distance of any point from it becomes straightforward.

Updated On: Jun 17, 2026

$2$
$1$
$4$
$3$

Show Solution

The Correct Option is B

Solution and Explanation

Was this answer helpful?

Top Questions on Conic sections

The area bounded by $ y - 1 = |x| $ and $ y + 1 = |x| $ is: (a) $ \frac{1}{2} $
- VITEEE - 2024
- Mathematics
- Conic sections
View Solution
Let the latus rectum of the hyperbola $ \frac{x^2}{9} - \frac{y^2}{b^2} = 1 $ subtend an angle of $ \frac{\pi}{3} $ at the center of the hyperbola. If $ b^2 $ is equal to $ \frac{1}{m} \left( 1 + \sqrt{n} \right) $, where $ l $ and $ m $ are coprime numbers, then $ l^2 + m^2 + n^2 $ is equal to $\_\_\_\_\_\_\_\_\_$.
- JEE Main - 2024
- Mathematics
- Conic sections
View Solution
Let $ e_1 $ be the eccentricity of the hyperbola $$ \frac{x^2}{16} - \frac{y^2}{9} = 1 $$ and $ e_2 $ be the eccentricity of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b, $$ which passes through the foci of the hyperbola. If $ e_1 e_2 = 1 $, then the length of the chord of the ellipse parallel to the x-axis and passing through (0, 2) is:
- JEE Main - 2024
- Mathematics
- Conic sections
View Solution
For $0 < \theta < \frac{pi}{2}$, if the eccentricity of the hyperbola $ x^2 - y^2 \csc^2 \theta = 5 $ is $ \sqrt{7} $ times the eccentricity of the ellipse $ x^2 \csc^2 \theta + y^2 = 5 $, then the value of $ \theta $ is:
- JEE Main - 2024
- Mathematics
- Conic sections
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in TS EAMCET exam

If $ f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right) $ is a real valued function then the range of $ f $ is

TS EAMCET - 2025
Algebra

View Solution

The range of the real valued function $ f(x)=\sin ^{-1}\left(\sqrt{x^{2}+x+1}\right) $ is

TS EAMCET - 2025
Algebra

View Solution

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

TS EAMCET - 2025
Algebra

View Solution

If the augmented matrix corresponding to the system of equations $ x+y-z=1 $, $ 2x+4y-z=0 $ and $ 3x+4y+5z=18 $ is transformed to $ \begin{bmatrix} 1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32 \end{bmatrix} $, then

TS EAMCET - 2025
Algebra

View Solution

The distance of the point \((1,2)\) from the directrix of the parabola \[ y^2-4x-4y+8=0 \] is:

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Conic sections

Questions Asked in TS EAMCET exam