AP EAMCET · Maths · Pair of Lines
The angle between the straight lines represented by \(\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2\) is
- A \(\frac{\alpha}{2}\)
- B \(\alpha\)
- C \(2\alpha\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(2\alpha\)
Step-by-step Solution
Detailed explanation
\((x^2+y^2) \sin^2 \alpha = (x \cos \alpha - y \sin \alpha)^2\) \(x^2 \sin^2 \alpha + y^2 \sin^2 \alpha = x^2 \cos^2 \alpha - 2xy \sin \alpha \cos \alpha + y^2 \sin^2 \alpha\) \(x^2 (\sin^2 \alpha - \cos^2 \alpha) + 2xy \sin \alpha \cos \alpha = 0\)…
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
- The derivative of \(e^{3 x} \sin 4 x\) with respect to \(x\), isAP EAMCET 2017 Easy
- If \(f\) is a relation from set of positive real number to the set of positive real numbers defined by \(f(x)=3 x^2-2\), then \(f\) isAP EAMCET 2022 Easy
- Through the point (4, 5), a straight line is drawn making positive intercepts on the coordinate axes. The area of the triangle thus
formed is least, when the ratio of the intercepts on the X and Y axes isAP EAMCET 2021 Medium - If \(z=\frac{\sqrt{3}+i}{2}\), then \(\left(z^{101}+i^{103}\right)^{105}=\)AP EAMCET 2018 Medium
- If a cylindrical vessel of given volume \(V\) with no lid on the top is to be made from a sheet of metal, then the radius \((r)\) and height \((h)\) of the vessel so that the metal sheet used is minimum, isAP EAMCET 2017 Hard
- \(\int\left(\frac{2-\sin 2 x}{1-\cos 2 x}\right) e^x d x\) is equal toAP EAMCET 2009 Easy
More PYQs from AP EAMCET
- Assertion (A): If heat of combustion of \(\mathrm{C}_2 \mathrm{H}_6\) is ' \(\mathrm{X}^{\prime} \mathrm{kJ} \mathrm{mol}^{-1}\), heat liberated on combustion of \(150 \mathrm{~g} \mathrm{C}_2 \mathrm{H}_6\) is \(\frac{\mathrm{X}}{5} \mathrm{~kJ}\).
Reason (R): Enthalpy is an extensive propertyAP EAMCET 2017 Medium - When the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the positive direction, an equation is transformed to \(x^2+y^2-6 x+8 y+21=0\). Then that original equation isAP EAMCET 2017 Medium
- If three non-zero real numbers \(a, b, c\) are in harmonic progression, then the straight lines \(\frac{x}{a}+\frac{y}{b}-\frac{2}{c}=0\) are concurrent at the pointAP EAMCET 2017 Hard
- The laser in an audio compact disc uses light of wavelength \(7.8 \times 10^2 \mathrm{~nm}\). What is the frequency of light emitted by laser?AP EAMCET 2023 Medium
- If the lines \(2 x-y+3=0\) and \(4 x+k y+3=0\) are conjugate with respect to the ellipse \(5 x^2+6 y^2-15=0\), then \(k\) equalsAP EAMCET 2021 Hard
- Identify chiral molecules from the following
AP EAMCET 2018 Medium