Question:
The tangents drawn at the extremeties of a focal chord of the parabola $y^2 = 16 x$
The tangents drawn at the extremeties of a focal chord of the parabola $y^2 = 16 x$
Updated On: Apr 13, 2024
- intersect on x = 0
- intersect on the line x + 4 = 0
- intersect at an angle of 60$^\circ$
- intersect at an angle of 45$^\circ$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Given equation is $y^2 = 16\,x$
Here, $\,\,\,\,\,\,a = 4$
As we know, that if tangents are drawn from an external points of a focal chord, then it will intersect on the directrix of the parabola.
$\therefore\,\,\,\,\, $ Equation of directrix is $x = - 4$
or $\,\,\,\,\,\,x + 4 = 0 $
Which is the required equation.
Here, $\,\,\,\,\,\,a = 4$
As we know, that if tangents are drawn from an external points of a focal chord, then it will intersect on the directrix of the parabola.
$\therefore\,\,\,\,\, $ Equation of directrix is $x = - 4$
or $\,\,\,\,\,\,x + 4 = 0 $
Which is the required equation.
Was this answer helpful?
1
0
Top Questions on Conic sections
- Consider the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\). Let S (p, q) be a point in the first quadrant such that \(\frac{p^2}{9}+\frac{q^2}{4}>1\). Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R be the vertex of the ellipse with positive x-coordinate and Obe the center of the ellipse. If the area of the triangle △ORT is \(\frac{3}{2}\) , then which of the following options is correct ?
- JEE Advanced - 2024
- Mathematics
- Conic sections
- The sum of squares of all possible values of $k$, for which the area of the region bounded by the parabolas \[2y^2 = kx \quad \text{and} \quad ky^2 = 2(y - x)\]is maximum, is equal to:
- JEE Main - 2024
- Mathematics
- Conic sections
- Let a conic \( C \) pass through the point \( (4, -2) \) and \( P(x, y), \, x \geq 3 \), be any point on \( C \). Let the slope of the line touching the conic \( C \) only at a single point \( P \) be half the slope of the line joining the points \( P \) and \( (3, -5) \). If the focal distance of the point \( (7, 1) \) on \( C \) is \( d \), then \( 12d \) equals ______.
- JEE Main - 2024
- Mathematics
- Conic sections
- Let \(S\) be the focus of the hyperbola \(\frac{x^2}{3} - \frac{y^2}{5} = 1\), on the positive x-axis. Let \(C\) be the circle with its centre at \(A\left(\sqrt{6}, \sqrt{5}\right)\) and passing through the point \(S\). If \(O\) is the origin and \(SAB\) is a diameter of \(C\), then the square of the area of the triangle \(OSB\) is equal to -
- JEE Main - 2024
- Mathematics
- Conic sections
- The parabola \( y^2 = 4x \) divides the area of the circle \( x^2 + y^2 = 5 \) in two parts. The area of the smaller part is equal to:
- JEE Main - 2024
- Mathematics
- Conic sections
View More Questions
Questions Asked in KCET exam
- Ten identical cells each emf 2V and internal resistance 1Ω are connected in series with two cells wrongly connected. A resistor of 10Ω is connected to the combination. What is the current through the resistor?
- KCET - 2023
- Cells in Series and in Parallel
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
View More Questions