WBJEE · Maths · Straight Lines
Let \(A\) be the point \((0,4)\) in the xy-plane and let \(B\) be the point \((2 t, 0)\). Let \(L\) be the midpoint of \(A B\) and let the perpendicular bisector of \(A B\) meet the \(y\)-axis \(M\). Let \(N\) be the midpoint of LM. Then locus of \(N\) is
- A a circle
- B a parabola
- C a straight line
- D a hyperbola
Answer & Solution
Correct Answer
(B) a parabola
Step-by-step Solution
Detailed explanation
Hint : Equation of LM \(\begin{aligned} & y-2=\frac{t}{2}(x-t) \\ & \Rightarrow M\left(0, \frac{4-t^2}{2}\right) \end{aligned}\) Midpoint of LM : N(h, k) \(\begin{aligned} & \Rightarrow \quad 2 h=t, 2 k=4-\frac{t^2}{2} \\ & \Rightarrow \quad x^2=2-y \end{aligned}\)
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 \(f:[0, \pi / 2) \rightarrow R\) is defined as
\(f(\theta)=\left|\begin{array}{ccc}1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1\end{array}\right|\) Then, the range of \(f\) isWBJEE 2015 Medium - Let \(S=\{(a, b, c) \in N \times N \times N: a+b+c=21\), \(a \leq b \leq c\}\) and \(T=\{(a, b, c) \in N \times N \times N: a, b, c\) are in \(A P \}\) where \(N\) is the set of all natural numbers. Then, the number of elements in the set \(\mathrm{S} \cap T\)WBJEE 2015 Easy
- For \(y=\sin ^{-1}\left\{\frac{5 x+12 \sqrt{1-x^{2}}}{13}\right\} ;|x| \leq 1\), if \(a\left(1-x^{2}\right) y_{2}+b x y_{1}=0\) then \((a, b)=\)WBJEE 2021 Medium
- If \(0 \lt \theta \lt \frac{\pi}{2}\) and \(\tan 3 \theta \neq 0\), then \(\tan \theta+\tan 2 \theta+\tan 3 \theta=0\) if \(\tan \theta \cdot \tan 2 \theta=\mathrm{k}\) where \(\mathrm{k}=\)WBJEE 2024 Medium
- Let \(f: R \rightarrow R\) be defined as \(f(x)=\frac{x^{2}-x+4}{x^{2}+x+4}\). Then, range of the function \(f(x)\) isWBJEE 2015 Medium
- A relation \(\rho\) on the set of real number \(R\) is defined as \(\{x \rho y: x y>0\} .\) Then, which of the following is/are true?WBJEE 2015 Easy
More PYQs from WBJEE
- A circular disc rolls on a horizontal Iloor without slipping and the centre of the disc moves with a uniform velocity \(v\). Which of the following values of the velocily at a point on the rim of the disc can have?WBJEE 2015 Medium
- When \(20 \mathrm{~g}\) of naphthoic acid \(\left(\mathrm{C}_{11} \mathrm{H}_{8} \mathrm{O}_{2}\right)\) is dissolved in \(50 \mathrm{~g}\) of benzene, a freezing point depression of \(2 \mathrm{~K}\) is observed. The vant Hoff factor (i) is \(\left[\mathrm{K}_{\mathrm{f}}=1.72^{\circ} \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}\right]\)WBJEE 2021 Easy
- The exact order of acidity of the compounds p-nitrophenol, acetic acid, acetylene and ethanol isWBJEE 2021 Medium
- If \(\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)\) where \(x\) and \(y\)
are real, then the ordered pair \((x, y)\) isWBJEE 2012 Medium - A simple pendulum, consisting of a small ball of mass \(m\) attached to a massless string hanging vertically from the ceiling, is oscillating with an amplitude such that \(T_{\max }=2 T_{\min }\) where \(T_{\max }\) and \(T_{\min }\) are the maximum and minimum tension in the string respectively. The value of maximum tension \(\mathrm{T}_{\max }\) in the string isWBJEE 2021 Medium
- A nucleus X emits a beta particle to produce a nucleus Y. If their atomic masses are \(\mathrm{M}_{\mathrm{x}}\) and \(\mathrm{M}_{\mathrm{y}}\) respectively, the maximum energy of the beta particle emitted is (where \(m_{e}\) is the mass of an electron and \(c\) is the velocity of light)WBJEE 2020 Easy