AP EAMCET · Maths · Ellipse
\(A B\) is a line segment moving between the axes such that ' \(A\) ' lies on \(X\)-axis and ' \(B\) ' lies on \(Y\)-axis. If \(P\) is a point on \(A B\) such that \(P A=b\) and \(P B=a\), then the equation of locus of \(P\) is
- A \(\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\)
- B \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
- C \(\frac{x^2}{2 a^2}+\frac{y^2}{2 b^2}=1\)
- D \(\frac{x^2}{2 b^2}+\frac{y^2}{a^2}=1\)
Answer & Solution
Correct Answer
(B) \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
Step-by-step Solution
Detailed explanation
\[ \text { Let } P(h, k) \text { be any point in the locus } \mathrm{cm} \] Let \(A=(x, 0), B=(0, y)\) Given, \(P A=b, P B=a\) In \(\triangle P M A\), \[ \sin \theta=\frac{k}{b} \] In \(\triangle B N P\), \[ \cos \theta=\frac{h}{a} \] We have,…
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 \(\quad \int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=f(x)-\log \left(1+x^2\right)\) then \(f(x)\) is equal toAP EAMCET 2005 Medium
- All the pairs \((x, y)\) that satisfy the inequality \(2^{\sqrt{\sin ^2 x-2 \sin x+5}}, \frac{1}{4\sin ^2 y} \leq 1\) also satisfy the equationAP EAMCET 2022 Medium
- If the harmonic mean between the roots of \((5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0\) is 4 , then the value of \(b\) isAP EAMCET 2013 Easy
- For the random variable with probability distribution is given by the table
The mean of isAP EAMCET 2021 Medium - The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are \((a, b),(a, c)\) and \((d, c)\), isAP EAMCET 2016 Easy
- \(\int 3^x\left(f^{\prime}(x)+f(x) \log 3\right) d x\) is equal toAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- The ground and first excited state energies are \(E_1\) and \(E_2\) respectively. Which pair of species has same energy? [Note that energy is indicated in the bracket].AP EAMCET 2017 Hard
- Find the equation of a circle which cuts the circle \(x^2+y^2-6 x+4 y-3=0\) orthogonally, while passing through \((3,0)\) and touching the \(Y\)-axis.AP EAMCET 2021 Easy
- Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.AP EAMCET 2022 Easy - In a \(100 \mathrm{~L}\) vessel, 3 moles of nitrogen and 3 moles of \(\mathrm{PCl}_5\) are taken and heated to \(500 \mathrm{~K}\). The equilibrium pressure is \(3.28 \mathrm{~atm}\). The percentage degree of dissociation of \(\mathrm{PCl}_5\) is : (Assume ideal behaviour for all gases).AP EAMCET 2017 Hard
- If \(y=\sqrt{\frac{x^4 \sqrt{3 x-5}}{\left(x^2-3\right)(2 x-3)}}\), then \(\left(\frac{d y}{d x}\right)_{x=2}=\)AP EAMCET 2025 Medium
- Total number of angular nodes of orbitals associated with third shell \((n=3)\) of an atom isAP EAMCET 2023 Easy