AP EAMCET · Maths · Straight Lines
The equation of the line, passing through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to the line \(x \cos\) \(\theta-y \sin \theta=a\), is
- A \(2 x \sin \theta+2 y \cos \theta=a \sin 2 \theta\)
- B \(x \cos \theta-y \sin \theta=a \sin 2 \theta\)
- C \(x \sin \theta+y \sin \theta=a \cos 2 \theta\)
- D \(x \sin \theta-y \cos \theta=a \cos 2 \theta\)
Answer & Solution
Correct Answer
(A) \(2 x \sin \theta+2 y \cos \theta=a \sin 2 \theta\)
Step-by-step Solution
Detailed explanation
Slope of line \(\mathrm{x} \cos \theta-\mathrm{y} \sin \theta=\mathrm{a}\) is \(\mathrm{m}^{\prime}=\cot \theta\) So, the slope of the required line is: \(m=\frac{-1}{m^{\prime}}=-\tan \theta\) Now, the required equation of line is:…
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 , then "" is equal toAP EAMCET 2021 Hard
- If \(\lim _{n \rightarrow \infty} \frac{1-(10)^n}{1+(10)^{n+1}}=\frac{-\alpha}{10}\), then \(\alpha\) is equal toAP EAMCET 2021 Medium
- \(\cos A=\frac{3}{4} \Rightarrow 32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5 A}{2}\right)=\)AP EAMCET 2011 Medium
- Match the following
Quadratic expression The minimum value (i) \(x^2-8 x+15\) (a) \(\quad \frac{7}{2}\) (ii) \(x^2-8 x+17\) (b) \(\quad-1\) (iii) \(2 x^2+4 x+7\) (c) 1 iv) \(\left(x+\frac{5}{3}\right)^2+\frac{7}{2}\) (d) 5 AP EAMCET 2017 Medium - The number of positive integers less than 10000 which contain the digit 5 atleast once isAP EAMCET 2025 Medium
- If \(\mathrm{S}_{\mathrm{n}}=1^3+2^3+\ldots. .+\mathrm{n}^3\) and \(\mathrm{T}_{\mathrm{n}}=1+2+\ldots. .+\mathrm{n}\), thenAP EAMCET 2025 Easy
More PYQs from AP EAMCET
- If \(\mathbf{a}\) and \(\mathbf{b}\) are two unit vectors and \(\theta\) is the angle between them, then the unit vector along the angular bisector of \(\mathbf{a}\) and \(\mathbf{b}\) is given byAP EAMCET 2020 Easy
- The area (in sq. units) bounded by \(x=4, y=-4\) and \(y=x\) isAP EAMCET 2023 Easy
- \(\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=\)AP EAMCET 2023 Medium
- A proton when accelerated through a potential difference of \(V\), has a de-Broglie wavelength \(\lambda\) associated with it. If an \(\alpha\)-particle is to have the same de-Broglie wavelength \(\lambda\), it must be accelerated through a potential difference ofAP EAMCET 2012 Easy
- A narrow slit of width 2 mm is illuminated with a monochromatic light of wavelength 500 nm. If the distance between the slit and the screen is 1 m, then first minima are separated by a distance ofAP EAMCET 2025 Easy
- If the circles \(x^2+y^2+2 \alpha x+2 y-8=0\) and \(x^2+y^2-2 x\) \(+\alpha y-14=0\) intersect orthogonally, then the distance between their centres isAP EAMCET 2024 Easy