TS EAMCET · Maths · Application of Derivatives
If the curves \(\frac{x^2}{4}+\frac{y^2}{9}=1\) and \(\frac{x^2}{16}-\frac{y^2}{k}=1\) cut each other orthogonally, then \(k=\)
- A 144
- B -9
- C 25
- D -21
Answer & Solution
Correct Answer
(D) -21
Step-by-step Solution
Detailed explanation
We have, \[ \frac{x^2}{4}+\frac{y^2}{9}=1 \text { and } \frac{x^2}{16}-\frac{y^2}{k}=1 \] On solving these equation, we get \[ x^2=\frac{144+16 k}{36+k} \text { and } y^2=\frac{-27 k}{36+k} \] Now, \(\quad \frac{x^2}{4}+\frac{y^2}{9}=1\)…
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
- Let \(A=\left|\begin{array}{cc}2 & e^{i \pi} \ -1 & i^{2012}\end{array}\right|, C=\frac{d}{d x}\left(\frac{1}{x}\right)_{x=1}\), \(D=\int_{e^2}^1 \frac{d x}{x}\) If the sum of two roots of the equation \(A x^3+B x^2+C x-D=0\) is equal to zero, then \(B\) is equal toTS EAMCET 2012 Medium
- When the origin is shifted to the point \(\left(\frac{3}{2}, \frac{3}{2}\right)\) by the translation of coordinate axes, then the transformed equation of \(32 x^2+8 x y+32 y^2-108 x-108 y+99=0\) isTS EAMCET 2020 Medium
- If \([2,6]\) is divided into four intervals of equal length, then the approximate value of \(\int_2^6 \frac{1}{x^2-x} d x\) using Simpson's rule, isTS EAMCET 2003 Hard
- If the Circumcenter of the triangle formed by the points \(A(a, 3), B(b, 5)\) and \(C(a, b)\) is \((1,1)\), then out of all the possible coordinates of \(\mathrm{C}\) the sum of the absolute values of the distinct coordinates of \(\mathrm{C}\) isTS EAMCET 2023 Easy
- The equation of the locus of a point whose distance from XY-plane is twice its distance from Z -axis isTS EAMCET 2025 Medium
- For the parabola \(y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}\) if the equation of directrix is \(y=k\), then \(k: h\)TS EAMCET 2020 Hard
More PYQs from TS EAMCET
- If the equation of the plane passing through the points \((2,1,2),(1,2,1)\) and perpendicular to the plane \(2 x-y+2 z=1\) is \(a x+b y+c z+d=0\) then \(\frac{a+b}{c+d}=\)TS EAMCET 2025 Medium
- The vectors \(\mathbf{A B}=3 \mathbf{i}-2 \mathbf{j}+2 \mathbf{k}\) and \(\mathbf{B C}=\mathbf{i}-2 \mathbf{k}\) are the adjacent sides of a parallelogram. The angle between its diagonals isTS EAMCET 2012 Medium
- The set of all real values of \(x\) for which the expansion of \(\left(125 x^2-\frac{27}{x}\right)^{-2 / 3}\) is valid, isTS EAMCET 2024 Medium
- If \(\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B\) and \(0^{\circ} \lt A+B \lt 270^{\circ}\), then \(A+B=\)TS EAMCET 2024 Medium
- Let \(L\) be the line parallel to the vector \(\sqrt{2} \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and passing through the point A given by \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\). If the distance between \(A\) and a point \(P\) on the line \(L\) is 18 units, then the position vector of such a point \(P\) isTS EAMCET 2019 Medium
- A liquid mixture is an ideal solution, if (i) It obeys ideal gas equation (ii) It obeys Raoult's law at all concentrations (iii) Solute - solute, solute - solvent and solvent - solvent interactions are similarTS EAMCET 2022 Easy