MHT CET · Maths · Pair of Lines
The angle between the lines \(y^{2} \sin ^{2} \theta-x y \sin ^{2} \theta+x^{2}\left(\cos ^{2} \theta-1\right)=0\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
We have \(y^{2} \sin ^{2} \theta-x y \sin ^{2} \theta+x^{2}\left(\cos ^{2} \theta-1\right)=0\)
\(\therefore\left(\sin ^{2} \theta\right) y^{2}-\left(\sin ^{2} \theta\right)(x y)-\left(\sin ^{2} \theta\right) x^{2}=0\)
\(\therefore\left(\sin ^{2} \theta\right)\left(y^{2}-x y-x^{2}\right)=0 \quad \Rightarrow \sin ^{2} \theta=0 \Rightarrow \theta=\frac{\pi}{2}\)
Note : sum of coefficients of \(x^{2}\) and \(y^{2}\) is zero.
\(\therefore\left(\sin ^{2} \theta\right) y^{2}-\left(\sin ^{2} \theta\right)(x y)-\left(\sin ^{2} \theta\right) x^{2}=0\)
\(\therefore\left(\sin ^{2} \theta\right)\left(y^{2}-x y-x^{2}\right)=0 \quad \Rightarrow \sin ^{2} \theta=0 \Rightarrow \theta=\frac{\pi}{2}\)
Note : sum of coefficients of \(x^{2}\) and \(y^{2}\) is zero.
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 \(\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})\) is false, then the truth values of \(p\) and \(q\) are respectivelyMHT CET 2024 Easy
- If the p.m.f. of a r.v. \(X\) is
then, the standard deviation of \(\mathrm{X}\) is (given \(p+q=1\) )MHT CET 2020 Easy - The circumradius of the triangle formed by the lines \(x y+2 x+2 y+4=0\) and \(x+y+2=0\) isMHT CET 2025 Medium
- For a real number \(x,[x]\) denotes the greatest integer less than or equal to \(x\). Then the value of
\(\left[\frac{1}{2}\right]+\left[\frac{1}{2}+\frac{1}{100}\right]+\left[\frac{1}{2}+\frac{2}{100}\right]+\left[\frac{1}{2}+\frac{3}{100}\right]+\ldots \ldots \ldots \ldots .+\left[\frac{1}{2}+\frac{99}{100}\right]=\)MHT CET 2025 Medium - The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face isMHT CET 2021 Medium
- If \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) are the angles of a cyclic quadrilateral taken in order, then \(\cos A+\cos B+\operatorname{Cos} C+\operatorname{Cos} D=\)MHT CET 2020 Easy
More PYQs from MHT CET
- Earth is assumed to be a charged conducting sphere having volume V and surface area \(A\). The capacitance of the earth in free space is ( \(\epsilon_0=\) permittivity of free space)MHT CET 2025 Medium
- Two waves \(y_1=0.35 \sin (316 t)\) and \(y_2=0.35 \sin (310 t)\) are propagating along the same direction. The number of beats produced per second areMHT CET 2022 Easy
- A \(A(3,2,-1)\) and \(B(1,4,3)\), then equation of the plane which bisects segment
AB perpendicularlyMHT CET 2020 Easy - If \(\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3\), then the derivative of \(\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2\) at \(x=1\) isMHT CET 2024 Hard
- If the function \(\mathrm{f}(x)=x^3+\mathrm{e}^{\frac{x}{2}}\) and \(\mathrm{g}(x)=\mathrm{f}^{-1}(x)\), then the value of \(g^{\prime}(1)\) isMHT CET 2024 Easy
- A first order reaction is given as \(A \rightarrow\) products. Its integrated equation isMHT CET 2011 Medium