WBJEE · Maths · Parabola
Let \(P\) be the point \((2,0)\) and \(Q\) be a variable point on \((y-6)^2=2(x-4)\). Then the locus of mid-point of \(P Q\) is
- A \(y^2+x+6 y+12=0\)
- B \(y^2-x+6 y+12=0\)
- C \(y^2+x-6 y+12=0\)
- D \(y^2-x-6 y+12=0\)
Answer & Solution
Correct Answer
(D) \(y^2-x-6 y+12=0\)
Step-by-step Solution
Detailed explanation
\[ \begin{gathered} \mathrm{P}(2,0) \\ \mathrm{Q}\left(4+\frac{1}{2} \mathrm{t}^2, 6+\mathrm{t}\right) \end{gathered} \] Let midpoint of \(\mathrm{PQ}\) be R(h, k)…
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 a particle moves in a straight line according to the law \(x=a \sin (\sqrt{\lambda} t+b)\), then the particle will come to rest at two points whose distance is [symbols have their usual meaning]WBJEE 2024 Medium
- If the co-efficients of \(x^2\) and \(x^3\) in the expansion of \((3+a x)^9\) be same, then the value of ' \(a\) ' isWBJEE 2009 Medium
- The roots of the quadratic equation \(x^2-2 \sqrt{3} x-22=0\) are :WBJEE 2010 Easy
- If \(U_n(n=1,2)\) denote the \(n^{\text {th }}\) derivative \((n=1,2)\) of \(U(x)=\frac{L x+M}{x^2-2 B x+C}(L, M, B, C\) are constants \()\), then \(P U_2+Q U_1\) \(+R U=0\), holds forWBJEE 2024 Medium
- In the interval \((-2 \pi, 0)\), the function \(f(x)=\sin \left(\frac{1}{x^3}\right)\)WBJEE 2023 Easy
- The value of the integral \(I=\int_{1 / 2014}^{2014} \frac{\tan ^{-1} x}{x} d x\) isWBJEE 2018 Medium
More PYQs from WBJEE
- Two particles, \(A\) and \(B\), having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii \(R_{1}\) and \(R_{2}\) resporctively. The ratio of the masses of \(A\) and \(B\) isWBJEE 2015 Medium
- The number of selection of \(n\) objects from \(2 n\) objects of which \(n\) are identical and the rest are different, isWBJEE 2018 Medium
- The \(\mathrm{H}_{3} \mathrm{O}^{+}\)ion has the following shapeWBJEE 2021 Easy
- Let \(S_{k}\) be the sum of an infinite GP series whose first term is \(k\) and common ratio is \(\frac{k}{k+1}(k>0)\) Then, the value of \(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{S_{k}}\) is equal toWBJEE 2012 Medium
- Let \(y=f(x)=2 x^{2}-3 x+2\). The differential of \(y\) when \(x\) changes from 2 to \(1.99\) isWBJEE 2020 Easy
- If \(\left(1+x+x^2+x^3\right)^5=\sum_{k=0}^{15} a_k x^k\) then \(\sum_{k=0}^7(-1)^k \cdot a_{2 k}\) is equal toWBJEE 2024 Medium