enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
For which of the following curves, the line \(x+\sqrt{3} y=2 \sqrt{3}\) is the tangent at the point \(\left(\frac{3 \sqrt{3}}{2}, \frac{1}{2}\right) \,?\)
- A \(x^{2}+y^{2}=7\)
- B \(y^{2}=\frac{1}{6 \sqrt{3}} x\)
- C \(2 x^{2}-18 y^{2}=9\)
- D \(x^{2}+9 y^{2}=9\)
Answer & Solution
Correct Answer
(D) \(x^{2}+9 y^{2}=9\)
Step-by-step Solution
Detailed explanation
\(m =-\frac{1}{\sqrt{3}}, c =2\) \((1)\) \(c = a \sqrt{1+ m ^{2}}\) \(c =\sqrt{7} \frac{2}{\sqrt{3}}\) (incorrect) \((2)\) \(c =\frac{ a }{ m }=\frac{\frac{1}{24 \sqrt{3}}}{\frac{-1}{\sqrt{3}}}=-\frac{1}{24}\) (incorrect) \((3)\) \(c =\sqrt{ a ^{2} m ^{2}- b ^{2}}\)…
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
- The value of \(\int_{-1}^{1} x ^{2} e ^{\left[x^{3}\right]} dx ,\) where \([ t ]\) denotes the greatest integer \(\leq t ,\) isJEE Mains 2021 Hard
- Let \(Q(a,b,c)\) be the image of the point \(P(3,2,1)\) in the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}.\) Then the distance of Q from the line \(\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}\) isJEE Mains 2026 Hard
- Let \( f(\alpha) \) denote the area of the region in the first quadrant bounded by \( x=0, x=1, y^{2}=x \) and \( y=|\alpha x-5|-|1-\alpha x|+\alpha x^{2}. \) Then \( (f(0)+f(1)) \) is equal toJEE Mains 2026 Hard
- Let for a triangle \(ABC\), \(\overline{A B}=-2 \hat{i}+\hat{j}+3 \hat{k}\) \(\overline{C B}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}\) \(\overline{C A}=4 \hat{i}+3 \hat{j}+\delta \hat{k}\) If \(\delta > 0\) and the area of the triangle \(ABC\) is \(5 \sqrt{6}\), then \(\overline{C B} \cdot \overline{C A}\) is equal toJEE Mains 2023 Hard
- Let \(f : R \rightarrow R\) be defined as, \(f(x)=\left\{\begin{array}{ll}-55 x, & \text { if } x<-5 \\ 2 x^{3}-3 x^{2}-120 x, & \text { if }-5 \leq x \leq 4 \\ 2 x^{3}-3 x^{2}-36 x-336, & \text { if } x>4\end{array}\right.\) Let \(A=\{ x \in R : f\) is increasing \(\} .\) Then \(A\) is equal to :JEE Mains 2021 Hard
- If \( y=y(x) \) satisfies the differential equation \( 16(\sqrt{x+9\sqrt{x}})(4+\sqrt{9+\sqrt{x}})cos~y~dy=(1+2~sin~y)dx, x>0 \) and \( y(256)=\frac{\pi}{2}, y(49)=\alpha \) then \( 2~sin~\alpha \) is equal to:JEE Mains 2026 Easy
More PYQs from JEE Mains
- If the tangent to the curve, \(y =f( x )= x \log _{ e } x\) \((x>0)\) at a point \((c, f(c))\) is parallel to the line segement joining the points \((1,0)\) and \(( e , e ),\) then \(c\) is equal toJEE Mains 2020 Medium
- Let \( f :R\rightarrow R \) be a twice differentiable function such that \( f^{\prime\prime}(x)>0 \) for all \( x\in R \) and \( f^{\prime}(a-1)=0 \), where a is real number. Let \( g(x)=f(tan^{2}x-2~tan~x+a), 0 < x < \frac{\pi}{2}\).
Consider the following two statements :
(I) g is increasing in \( (0,\frac{\pi}{4}) \)
(II) g is decreasing in \( (\frac{\pi}{4},\frac{\pi}{2}) \)
Then,JEE Mains 2026 Easy - Statement \(- 1:\) The function \(x^2 (e^x + e^{-x})\) is increasing for all \(x > 0.\) Statement \(-2:\) The functions \(x^2e^x\) and \(x^2e^{-x}\) are increasing for all \(x > 0\) and the sum of two increasing functions in any interval \((a, b)\) is an increasing function in \((a, b).\)JEE Mains 2013 Hard
- The number of matrices \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), where a \(, b, c, d \in\{-1,0,1,2,3, \ldots \ldots, 10\}\), such that \(A=A^{-1}\), isJEE Mains 2022 Hard
- Let a function \(f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)\) be defined by \(f\left( x \right) = \left| {1 - \frac{1}{x}} \right|\). Then \(f\) isJEE Mains 2019 Hard
- If \(z\) is a complex number such that \(\frac{z-i}{z-1}\) is purely imaginary, then the minimum value of \(\mid \mathrm{z}-(3+3 \mathrm{i}) \mid\) is :JEE Mains 2021 Hard