AP EAMCET · Maths · Hyperbola
If the line \(3 x-m y+5=0\) is a tangent to the hyperbola \(3 x^2-4 y^2=300\) then the square of the \(Y-\) intercept made by this tangent line is
- A \(\frac{25}{3}\)
- B \(\frac{35}{3}\)
- C \(\frac{45}{7}\)
- D \(\frac{15}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{15}{7}\)
Step-by-step Solution
Detailed explanation
\(3 x^2-4 y^2=300\) \[ \frac{x^2}{100}-\frac{y^2}{75}=1 \] and \(3 x-m y+5=0 \Rightarrow y=\frac{3}{m} x+\frac{5}{m}\) Now, for condition of tangents:…
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 \(f^{\prime}(x)=|x|\) and \(g(x)=|x|+a,(a>0)\). For \(0 \leq x \leq b\), \(\{(x, y) / g(x) \leq y \leq f(x)\}\) represents all the points in the interior ofAP EAMCET 2023 Medium
- If the function \(f\) defined by
\[
f(x)=\left\{\begin{array}{llc}
\cos x, & \text { if } & x \leq 0 \\
3 x+\alpha, & \text { if } & 0 < x < 2 \\
\beta x+3, & \text { if } & 2 \leq x \leq 4 \\
11, & \text { if } & x>4
\end{array}\right.
\]
where, \(\alpha\) and \(\beta\) are real constants, is continuous on \(R\), then \(\alpha^2+\beta^2=\)AP EAMCET 2018 Easy - If \(f(x)=a \log |x|+b x^2+x\) has extreme values at \(x=-1\) and \(x=2\), then the ordered pair \((a, b)=\)AP EAMCET 2019 Medium
- The line \(x=m^2\) meets an ellipse \(9 x^2+y^2=9\) in the real and distinct points if and only ifAP EAMCET 2020 Easy
- If \(\alpha, \beta\) and \(\gamma\) are the root of the equation \(x^3-6 x^2+11 x+6=0\), then \(\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2\) is equal toAP EAMCET 2021 Easy
- If \(\mathbf{P Q}+\mathbf{Q R}=\left(2 \lambda^2-5\right) \mathbf{R P}\) then, \(\lambda\) is equal toAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- Two rectangular blocks of masses and are connected by a string and kept on a frictionless horizontal table. If a force of is applied on block away from block, then the tension in string isAP EAMCET 2022 Easy
- In which of the following sets of molecules, the central atoms of molecules have same hybridisation?AP EAMCET 2024 Easy
- In Young's double slit experiment the slits are horizontal. The intensity at a point ' \(\mathrm{P}\) ' on the screen shown in the figure is \(\frac{\mathrm{I}_0}{4}\) where \(\mathrm{I}_0\) is maximum intensity. If the distance between the two slits \(S_1\) and \(S_2\) is \(2 \lambda\), then the value of ' \(\theta\) ' is
AP EAMCET 2017 Medium - \(x=\frac{1}{2}\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal toAP EAMCET 2005 Medium
- Two short bar magnets of moments ' \(\mathrm{M}\) ' and ' \(\sqrt{3} \mathrm{M}\) ' are joined like a cross (+). This cross is suspended from its centre with its plane horizontal in the earth's magnetic field. When the cross comes to equilibrium, angle made by the weaker magnet with the earth's magnetic field \(B_H\) isAP EAMCET 2017 Medium
- Two persons \(A\) and \(B\) throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game: then the probability that \(B\) wins the game isAP EAMCET 2024 Medium