TS EAMCET · Maths · Straight Lines
A line segment joining a point A on \(x\)-axis to a point B on \(y\)-axis is such that \(\mathrm{AB}=15\). If P is a point on AB such that \(\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{2}{3}\) then the locus of P is
- A \(x=9 \cos \theta, y=6 \sin \theta\)
- B \(x=6 \cos \theta, y=9 \sin \theta\)
- C \(x=6 \cos \theta, y=6 \sin \theta\)
- D \(x=9 \cos \theta, y=9 \sin \theta\)
Answer & Solution
Correct Answer
(A) \(x=9 \cos \theta, y=6 \sin \theta\)
Step-by-step Solution
Detailed explanation
\(x = \frac{3a+2(0)}{5} = \frac{3a}{5}, y = \frac{3(0)+2b}{5} = \frac{2b}{5}\) \(a=\frac{5x}{3}, b=\frac{5y}{2}\) \(a^2+b^2 = 15^2\) \(\left(\frac{5x}{3}\right)^2 + \left(\frac{5y}{2}\right)^2 = 225\) \(\frac{25x^2}{9} + \frac{25y^2}{4} = 225\)…
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 the circle \(S_1: x^2+y^2=16\) intersects another circle \(S_2\) of radius 5 units such that the common chord is of maximum length and slope \(\frac{3}{4}\), then the centre of the circle \(S_2\) isTS EAMCET 2020 Hard
- If \(f(x)=\sqrt{x}(x \geq 0)\) and \(g(x)=1+x^2\), then \((f o g)^{\prime}(1)=\)TS EAMCET 2023 Medium
- Let \([A]_{3 \times 3}\) be a non-singular matrix such that \(A^{-1}=\frac{1}{3}\left(A^2-5 A+7 I\right)\).
Then \(17 A^8-85 A^7+119 A^6-51 A^5-19 A^4\) \(+95 A^3-133 A^2+58 A+I=\)TS EAMCET 2020 Medium - For \(0 < x \leq \pi, \sinh ^{-1}(\cot x)\) is equal toTS EAMCET 2011 Medium
- If \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal toTS EAMCET 2005 Hard
- If the position vectors of the points \(A, B, C, D\) given by \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\), \(\frac{1}{4}(7 \hat{\mathbf{i}}+15 \hat{\mathbf{j}}+15 \hat{\mathbf{k}}) \text { and } \frac{1}{3}[7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+(5+3 a) \hat{\mathbf{k}}]\) respectively are such that \(|\mathbf{A C}|=|\mathbf{B D}|\), then \(16(3 a-1)^2=\)TS EAMCET 2019 Medium
More PYQs from TS EAMCET
- A proton, a deuteron (nucleus of \({ }_1 \mathrm{H}^2\) ) and an \(\alpha\)-particle with same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is :TS EAMCET 2006 Easy
- Let \(n=1 !+4 !+7 !+\ldots+400 !\). Then ten's digit of \(n\) isTS EAMCET 2010 Hard
- The rate of attack of an electrophile is least when \(\mathrm{X}\) in the given compound is
TS EAMCET 2023 Easy - A point mass is located at a distance from a uniform thin rod of mass and length as shown in the figure. The magnitude of gravitational force of attraction is
TS EAMCET 2021 Hard - If and are orthogonal vectors and makes an obtuse angle with -axis, thenTS EAMCET 2020 Easy
- Let one of the sides of a triangle be \(17 \mathrm{~cm}\) and the sum of all the sides of the triangle be \(40 \mathrm{~cm}\). If the sum of two adjacent sides is \(35 \mathrm{~cm}\), then the area (in sq. cms) of the triangle isTS EAMCET 2019 Easy