TS EAMCET · Maths · Circle
If \(x=\frac{2 a t}{1+t^2}, y=\frac{a\left(1-t^2\right)}{1+t^2}\), where \(t\) is a parameter, then \(a\) is
- A the length of the latusrectum of a parabola
- B the radius of a circle
- C the length of the transverse axis of a hyperbola
- D the length of the semi-major axis of an ellipse
Answer & Solution
Correct Answer
(B) the radius of a circle
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & x=\frac{2 a t}{1+t^2} \\ & y=\frac{a\left(1-t^2\right)}{1+t^2} \end{aligned} \] put \(t=\tan \theta\), We get \[ x=a \sin 2 \theta, y=a \cos 2 \theta \] Squaring and adding we get \[ x^2+y^2=a^2 \] \(\therefore a\) is radius of circle.
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
- In a \(\triangle A B C\), if \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\), then \(\triangle A B C\) isTS EAMCET 2011 Medium
- \(x-2 y-6=0\) is a normal to the circle \(x^2+y^2+2 g x+2 f y-8=0\). If the line \(y=2\) touches this circle, then the radius of the circle can beTS EAMCET 2024 Medium
- \(\int \frac{\cos 2 x \cdot \sin 4 x}{\cos ^4 x\left(1+\cos ^2 2 x\right)} d x=\)TS EAMCET 2018 Medium
- Let \(A=\{x \in R /|\sqrt{3} \cos x-\sin x| \geq 2,0 \leq x \leq 2 \pi\}\). If \(x_1 \in A, x_2 \in A\), then \(\frac{x_1}{x_2}=\)TS EAMCET 2018 Easy
- If \(\mathrm{X} \sim \mathrm{B}(7, \mathrm{p})\) is a binomial variate and \(\mathrm{P}(\mathrm{X}=3)=\mathrm{P}(\mathrm{X}=5)\) then \(\mathrm{p}=\)TS EAMCET 2025 Medium
- If the roots \(\alpha, \beta, \gamma\) of the equation \(x^3-6 x^2+p x+10=0\) are in arithmetic progression, then \(\alpha^3+\beta^3+\gamma^3=\)TS EAMCET 2019 Medium
More PYQs from TS EAMCET
- The area (in sq units) of the quadrilateral formed by two pairs of lines \(\lambda^2 x^2-m^2 y^2-n(\lambda x+m y)=0 \quad\) and \(\lambda^2 x^2-m^2 y^2+n(\lambda x+m y)=0\) is:TS EAMCET 2003 Hard
- If \(A=\left[\begin{array}{ccc}1 & -3 & -5 \\ -2 & 4 & -6 \\ 7 & -11 & 13\end{array}\right]\), then \(\sqrt{|\operatorname{Adj} A|}=\)TS EAMCET 2025 Medium
- If a radioactive substance decays \(10 \%\) in every 16 hours, then the percentage of the radioactive substance that remains after 2 days isTS EAMCET 2025 Medium
- If where thenTS EAMCET 2021 Easy
- If the length of the chord \(2 x+3 y+\mathrm{k}=0\) of the circle \(x^2+y^2-2 x+4 y-11=0\) is \(2 \sqrt{3}\), then the sum of all possible values of \(k\) isTS EAMCET 2025 Medium
- If \(y=\frac{\tan x \cos ^{-1} x}{\sqrt{1-x^2}}\) then the value of \(\frac{d y}{d x}\), when \(x=0\) isTS EAMCET 2024 Easy