WBJEE · Maths · Parabola
\(\triangle O A B\) is an equilateral triangle inscribed in the parabola \(y^2=4 a x, a\gt0\) with \(O\) as the vertex, then the length of the side of \(\triangle \mathrm{OAB}\) is
- A \(8 \mathrm{a} \sqrt{3}\) unit
- B 8 a unit
- C \(4 \mathrm{a} \sqrt{3}\) unit
- D 4a unit
Answer & Solution
Correct Answer
(A) \(8 \mathrm{a} \sqrt{3}\) unit
Step-by-step Solution
Detailed explanation
Hint : Slope of \(O A: M_{O A}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}\) Equation of \(O A: y=\frac{1}{\sqrt{3}} x\) from parabola and line \(O A, \frac{x^2}{3}=4 a x\) \(\Rightarrow x=12 a \Rightarrow y=4 \sqrt{3} a \therefore A B=2 \times 4 \sqrt{3} a=8 a \sqrt{3}\) unit
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
- A line passes through the point \((-1,1)\) and makes an angle \(\sin ^{-1}\left(\frac{3}{5}\right)\) in the positive direction of \(x\)-axis. If this line meets the curve \(x^2=4 y-9\) at \(A\) and \(B\), then \(|A B|\) is equal toWBJEE 2022 Easy
- If \(A\) and \(B\) are coefficients of \(x^{\mathrm{n}}\) in the expansions of \((1+x)^{2 \mathrm{n}}\) and \((1+x)^{2 \mathrm{n}-1}\) respectively, then \(\mathrm{A} / \mathrm{B}\) is equal toWBJEE 2011 Medium
- If \(a, b, c\) are in A.P. and if the equations \((b-c) x^2+(c-a) x+(a-b)=0\) and \(2(c+a) x^2+(b+c) x=0\) have a common root, thenWBJEE 2025 Hard
- The coefficient of \(a^{10} b^7 c^3\) in the expansion of \((b c+c a+a b)^{10}\) isWBJEE 2024 Medium
- If \(\mathrm{P}(\mathrm{x})=a \mathrm{x}^{2}+\mathrm{bx}+\mathrm{c}\) and \(\mathrm{Q}(\mathrm{x})=-\mathrm{ax}^{2}+\mathrm{dx}+\mathrm{c}\), where \(\mathrm{ac} \neq 0 \quad[\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\) are all real], then \(\mathrm{P}(\mathrm{x}) \cdot \mathrm{Q}(\mathrm{x})=0\) hasWBJEE 2020 Medium
- If \(f(x)=\int_0^{\sin ^2 x} \sin ^{-1} \sqrt{t}\) \(dt\) and \(g(x)=\int_0^{\cos ^2 x} \cos ^{-1} \sqrt{t}\) \(dt\), then the value of \(f(x)+g(x)\) isWBJEE 2025 Medium
More PYQs from WBJEE
- Angle between \(\mathrm{y}^2=\mathrm{x}\) and \(\mathrm{x}^2=\mathrm{y}\) at the origin isWBJEE 2009 Medium
- Let \(z_{1}, z_{2}\) be two fixed complex numbers in the argand plane and \(z\) be an arbitrary point satisfying \(\left|z-z_{1}\right|+\left|z-z_{2}\right|=2\left|z_{1}-z_{2}\right|\). Then, the locus of \(z\) will beWBJEE 2014 Hard
- The locus of the middle points of all chords of the parabola \(y^2=4\) ax passing through the vertex isWBJEE 2011 Easy
- If \(\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2},\) then the value of \(x\) isWBJEE 2014 Easy
- If \(\log _3 x+\log _3 y=2+\log _3 2\) and \(\log _3(x+y)=2\), thenWBJEE 2011 Easy
- Each of \(a\) and \(b\) can take values 1 or 2 with equal probability. The probability that the equation \(a x^{2}+b x+1=0\) has real roots, is equal toWBJEE 2013 Easy