TS EAMCET · Maths · Hyperbola
If the tangent drawn at a point \(\mathrm{P}(t)\) on the hyperbola \(x^2-y^2=c^2\) cuts \(X\)-axis at T and the normal drawn at the same point \(P\) cuts the Y -axis at N , then the equation of the locus of the midpoint of TN is
- A \(\frac{c^2}{4 x^2}-\frac{y^2}{c^2}=1\)
- B \(\frac{x^2}{c^2}-\frac{y^2}{4 c^2}=1\)
- C \(\frac{x^2}{4 c^2}+\frac{y^2}{c^2}=1\)
- D \(x^2+y^2=4 c^2\)
Answer & Solution
Correct Answer
(A) \(\frac{c^2}{4 x^2}-\frac{y^2}{c^2}=1\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{P}(\mathrm{t})=\mathrm{ct}\) Then \(\left(c t, \sqrt{c^2 t^2-c^2}\right)\) lies on hyperbola \(x^2-y^2=c^2\) Equation of tangent \(=x c t-y\left(\sqrt{c^2 t^2-c^2}\right)=c^2\) x -intercept of tangent \(=\mathrm{T}=\frac{c}{t}\) Equation of normal…
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
- If \(\frac{6 x^4+13 x^3+2 x^2-x+3}{2 x^2+3 x-2}=f(x)+\frac{A}{a x-1}+\frac{B}{x+b}\) then \(f(1)+a \cdot B+b \cdot A=\)TS EAMCET 2023 Medium
- The approximate value of \(\int_1^3 \frac{d x}{2+3 x}\) using Simpson's rule and dividing the interval \([1,3]\) into two equal parts isTS EAMCET 2013 Hard
- An equilateral triangle is inscribed in the parabola \(y^2=16 a x\) with one of its vertices at the origin. Then, the centroid of that triangle isTS EAMCET 2018 Easy
- The product of the perpendicular distances from any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) to its asymptotes isTS EAMCET 2010 Medium
- \(\left|\begin{array}{lll}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{array}\right|\) is equal toTS EAMCET 2011 Easy
- The solution set of \((5+4 \cos \theta)(2 \cos \theta+1)=0\) in the interval \([0,2 \pi]\), is :TS EAMCET 2003 Medium
More PYQs from TS EAMCET
- The equation of the normal at \(t=\frac{\pi}{2}\) to the curve \(\mathrm{x}=\) \(2 \sin t, y=2 \cos t\) isTS EAMCET 2023 Easy
- The positive integer \(n \leq 5\) for which \(\int_0^1 e^x(x-1)^n d x=16-6 e\) isTS EAMCET 2020 Medium
- The electrochemical equivalent of a metal is ' \(x\) ' \(g\) coulomb \({ }^{-1}\). The equivalent weight of metal isTS EAMCET 2004 Easy
- Let \(S_r=\{x, y, z) / x+y+z=11, x \geq r, y \geq r\), \(z \geq r, x, y, z, r\) are integers \(\}\) and \(n\left(S_r\right)\) represents the number of elements in \(S_r\). Then \(n\left(S_{2)}+n\left(S_3\right)+n\left(S_4\right)=\right.\)TS EAMCET 2020 Easy
- If the \(k^{\text {th }}\) term in the expansion of \(\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^6\) is independent of \(x\), then the numerically greatest term in the expansion of \(\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^k\) when \(x=\frac{2}{3}\), isTS EAMCET 2019 Medium
- Let \(\alpha\) be a common root of the equations \(x^3-2 x-25 \lambda=0\), \(3 x^3-8 x-\frac{175}{3} \lambda=0\) and \(\lambda>0\). Then \(\lambda=\)TS EAMCET 2022 Medium