AP EAMCET · Maths · Parabola
The equation of the tangent to the parabola \(y^2=12 x\), which makes an angle \(30^{\circ}\) with the positive direction of \(X\)-axis is given by \(x-\sqrt{3} y+9=0\), then its points of contact is
- A \((-9,-6 \sqrt{3})\)
- B \((9,-6 \sqrt{3})\)
- C \((-9,6 \sqrt{3})\)
- D \((9,6 \sqrt{3})\)
Answer & Solution
Correct Answer
(D) \((9,6 \sqrt{3})\)
Step-by-step Solution
Detailed explanation
Let the point of tangency of tangent \(x-\sqrt{3} y+9=0\) to the parabola \(y^2=12 x\) is \(\left(x_1 y_1\right)\). Since equation of tangent to the parabola \(y^2=12 x\) at point \(\left(x_1, y_1\right)\) is \(y y_1=6\left(x+x_1\right)\) \(6 x-y_1 y+6 x_1=0\), which represent…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(\alpha \in \mathbb{R}\). If the line \((\alpha+1) x+\alpha y+\alpha=1\) passes through a fixed point \((h, k)\) for all \(\alpha\), then \(h^2+k^2=\)AP EAMCET 2024 Easy
- The general solution of the equation \(\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x\) isAP EAMCET 2025 Medium
- Let \(A\) and \(B\) be two events with \(P(A)=\frac{1}{7}\), \(P\left(\frac{A}{B}\right)=\frac{2}{3}\) and \(P(B)=\frac{2}{7}\). Then, the value \(P\left(\frac{B}{A}\right)\) isAP EAMCET 2021 Easy
- The sum of the series
\(\frac{3}{4 \cdot 8}-\frac{3 \cdot 5}{4 \cdot 8 \cdot 12}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16}-\ldots\)AP EAMCET 2007 Hard - For \(a \neq 0\), if the sum of the distances of a point from the points \((a, 0,0)\) and \((-a, 0,0)\) is a constant \(2 \mathrm{k}\), then the locus of that point isAP EAMCET 2018 Easy
- Find the sum of the order and degree of the differential equation \(y=x\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}\)AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The structure of solids is investigated by usingAP EAMCET 2024 Easy
- If , thenAP EAMCET 2020 Easy
- Five current carrying conductors meet at a point . What is the magnitude and direction of the current in the fifth conductor?
AP EAMCET 2021 Medium - The rank of the matrix \(\left[\begin{array}{cccc}2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4\end{array}\right]\) isAP EAMCET 2025 Medium
- \(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) then \(A^3-4 A^2-6 A\) is equal to :AP EAMCET 2006 Medium
- The rms value of the electric field of an electromagnetic wave emitted by a source is \(660 \mathrm{NC}^{-1}\). The average energy density of the electromagnetic wave isAP EAMCET 2024 Easy