If $ x - y - 3 = 0 $ is a normal drawn through the point $ (5, 2) $ to the parabola $ y^2 = 4x $, then the slope of the other normal that can be drawn through the same point to the parabola is?
Show Hint
- 0
- -1
- 2
- -2
The Correct Option is D
Solution and Explanation
Top Questions on Conic sections
- The roots of the quadratic equation \( x^2 - 16 = 0 \) are:
- TS POLYCET - 2025
- Mathematics
- Conic sections
- If $ \theta $ is the angle subtended by a latus rectum at the center of the hyperbola having eccentricity $$ \frac{2}{\sqrt{7} - \sqrt{3}}, $$ then find $ \sin \theta $.
- AP EAPCET - 2025
- Mathematics
- Conic sections
- The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola $$ \frac{x^2}{4} - \frac{y^2}{5} = 1 $$ meets the x-axis and y-axis at $ A $ and $ B $ respectively. If $ O $ is the origin, find $$ (OA)^2 - (OB)^2. $$
- AP EAPCET - 2025
- Mathematics
- Conic sections
- If the normal drawn at the point $$ P \left(\frac{\pi}{4}\right) $$ on the ellipse $$ x^2 + 4y^2 - 4 = 0 $$ meets the ellipse again at $ Q(\alpha, \beta) $, then find $ \alpha $.
- AP EAPCET - 2025
- Mathematics
- Conic sections
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?
- JEE Advanced - 2025
- Mathematics
- Conic sections
Questions Asked in AP EAPCET exam
- Two blocks of masses 8 kg and 12 kg kept on a smooth horizontal table are connected to the ends of a light string as shown in the figure. If a horizontal force of 500 N is applied to the block of mass 12 kg, then the tension in the string connecting the blocks is
- AP EAPCET - 2025
- laws of motion
- If the normal drawn to the hyperbola \( xy = 16 \) at (8, 2) meets the hyperbola again at a point \((\alpha, \beta)\), then \( |\beta| + \frac{1}{|\alpha|} = \)
- AP EAPCET - 2025
- Hyperbola
- If the binding energy per nucleon of deuteron (\( ^1\mathrm{H}^2 \)) is 1.15 MeV and an \(\alpha\)-particle has a binding energy of 7.1 MeV per nucleon, then the energy released per nucleon in the given reaction is \[ ^1\mathrm{H}^2 + ^1\mathrm{H}^2 \rightarrow ^2\mathrm{He}^4 + Q \]
- AP EAPCET - 2025
- Nuclear physics
- If the function \( f \) defined by \[ f(x) = \begin{cases} \dfrac{1 - \cos 4x}{x^2}, & x<0 \\ a, & x = 0 \\ \dfrac{\sqrt{x}}{\sqrt{16 + \sqrt{x}} - 4}, & x>0 \end{cases} \] is continuous at \( x = 0 \), then \( a = \)
- AP EAPCET - 2025
- Limits and Exponential Functions
If \( \vec{u}, \vec{v}, \vec{w} \) are non-coplanar vectors and \( p, q \) are real numbers, then the equality:
\[ [3\vec{u} \quad p\vec{v} \quad p\vec{w}] - [p\vec{v} \quad \vec{w} \quad q\vec{u}] - [2\vec{w} \quad q\vec{v} \quad q\vec{u}] = 0 \]
holds for:
- AP EAPCET - 2025
- Geometry and Vectors
