enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the point \(P\) on the curve, \(4 x^{2}+5 y^{2}=20\) is farthest from the point \(Q (0,-4),\) then \(PQ ^{2}\) is equal to
- A \(21\)
- B \(36\)
- C \(48\)
- D \(29\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
Given ellipse is \(\frac{x^{2}}{5}+\frac{y^{2}}{4}=1\) Let point \(P\) is \((\sqrt{5} \cos \theta, 2 \sin \theta)\) \(( PQ )^{2}=5 \cos ^{2} \theta+4(\sin \theta+2)^{2}\) \(( PQ )^{2}=\cos ^{2} \theta+16 \sin \theta+20\) \(( PQ )^{2}=-\sin ^{2} \theta+16 \sin \theta+21\)…
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 solution curve of the differential equation \(\left(y-2 \log _e x\right) d x+\left(x \log _e x^2\right) d y=0, x > 1\) passes through the points \(\left(e, \frac{4}{3}\right)\) and \(\left(e^4, \alpha\right)\), then \(\alpha\) is equal to \(................\).JEE Mains 2023 Hard
- Let \(a_1, a_2, a_3, ……\) be and \(A.P\) with \(a_6 = 2.\) Then the common difference of this \(A.P.,\) which maximizes the product \(a_1a_4a_5\) isJEE Mains 2019 Hard
- Let \(A=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]\). If \(M\) and \(N\) are two matrices given by \(M =\sum \limits_{ k =1}^{10} A ^{2 k }\) and \(N =\sum \limits_{ k =1}^{10} A ^{2 k -1}\) then \(MN ^{2}\) isJEE Mains 2022 Medium
- Let \( f(x)=\int\frac{(2-x^{2})e^{x}}{(\sqrt{1+x})(1-x)^{\frac{3}{2}}}dx \). If \( f(0)=0 \), then \( f(\frac{1}{2}) \) is equal to:JEE Mains 2026 Easy
- Let for some function \(\mathrm{y}=f(x), \int_0^x t f(t) d t=x^2 f(x), x\gt0\) and \(f(2)=3\). Then \(f(6)\) is equal toJEE Mains 2025 Medium
- A value of \(\theta \in (0, \pi /3)\), for which \(\left| {\begin{array}{*{20}{c}}
{1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\
{{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta }
\end{array}} \right| = 0\), isJEE Mains 2019 Hard
More PYQs from JEE Mains
- In a increasing geometric series, the sum of the second and the sixth term is \(\frac{25}{2}\) and the product of the third and fifth term is \(25 .\) Then, the sum of \(4^{\text {th }}, 6^{\text {th }}\) and \(8^{\text {th }}\) terms is equal toJEE Mains 2021 Hard
- Let \(A=\left(\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right),\) where \([t]\) denotes the greatest integer less than or equal to \(\mathrm{t}\). If \(\operatorname{det}(\mathrm{A})=192\), then the set of values of \(\mathrm{x}\) is the intervalJEE Mains 2021 Hard
- The angle of elevation of the top of a vertical tower from a point \(A\), due east of it is \(45^o\) . The angle of elevation of the top of the same tower from a point \(B\). due south of \(A\) is \(30^o\). If the distance between \(A\) and \(B\) is \(54\sqrt 2 \,m\), then the height of the tower (in metres), isJEE Mains 2016 Hard
- Let \(S=\{1,2,3,4,5,6,7,8,9\}\). Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,JEE Mains 2026 Medium
- If the function \(f\) defined as \(f(x)\, = \frac{1}{x} - \frac{{k - 1}}{{{e^{2x}} - 1}}\) ,\(x\, \ne \,0,\) is continuous at \(x = 0.\) then the ordered pair \((k,f(0))\) is equal to?JEE Mains 2018 Hard
- A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let \(P\) be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of \(P\) isJEE Mains 2014 Hard