JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the tangent to the parabola \(S: y^{2}=2 x\) at the point \(P(2,2)\) meet the \(x\)-axis at \(Q\) and normal at it meet the parabola \(S\) at the point \(R\). Then the area (in \(sq.\, units\)) of the triangle \(P Q R\) is equal to:
- A \(25\)
- B \(\frac{25}{2}\)
- C \(\frac{15}{2}\)
- D \(\frac{35}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{25}{2}\)
Step-by-step Solution
Detailed explanation
Tangent at \(\mathrm{P}: \mathrm{y}(2)=2(1 / 2)(\mathrm{x}+2)\) \(\Rightarrow 2 y=x+2\) \(\therefore Q=(-2,0)\) Normal at \(\mathrm{P}: \mathrm{y}-2=-\frac{(2)}{2.1 / 2}(x-2)\) \(\Rightarrow y-2=-2(x-2)\) \(\Rightarrow y=6-2 x\) \(\therefore\) Solving with…
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
- Let \(\overrightarrow{\mathrm{OA}}=2 \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{OB}}=6 \overrightarrow{\mathrm{a}}+5 \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{OC}}=3 \overrightarrow{\mathrm{b}}\), where \(O\) is the origin. If the area of the parallelogram with adjacent sides \(\overrightarrow{\mathrm{OA}}\) and \(\overrightarrow{\mathrm{OC}}\) is \(15\) sq. units, then the area (in sq. units) of the quadrilateral \(\mathrm{OABC}\) is equal to :JEE Mains 2024 Medium
- Let \({\left( { - \,2\, - \,\frac{1}{3}\,i} \right)^3} = \frac{{x \,+ \,iy}}{{27}}(i\, = \,\sqrt { - 1} ),\) where \(x\) and \(y\) are real numbers, then \(y -x\) equalsJEE Mains 2019 Hard
- The function \(f(x)=x^{3}-6 x^{2}+a x+b\) is such that \(f(2)=f(4)=0\). Consider two statements. \((S_1)\) there exists \(\mathrm{x}_{1}, \mathrm{x}_{2} \in(2,4), \mathrm{x}_{1}<\mathrm{x}_{2}\), such that \(f^{\prime}\left(x_{1}\right)=-1\) and \(f^{\prime}\left(x_{2}\right)=0\) \((S_2)\) there exists \(\mathrm{x}_{3}, \mathrm{x}_{4} \in(2,4), \mathrm{x}_{3}<\mathrm{x}_{4}\), such that \(f\) is decreasing in \(\left(2, x_{4}\right)\), increasing in \(\left(x_{4}, 4\right)\) and \(2 f^{\prime}\left(x_{3}\right)=\sqrt{3} f\left(x_{4}\right)\). ThenJEE Mains 2021 Hard
- If \(\displaystyle\int_{\pi/6}^{\pi/4}\left(\cot\left(x-\dfrac{\pi}{3}\right)\cot\left(x+\dfrac{\pi}{3}\right)+1\right)dx = \alpha\log_e(\sqrt{3}-1)\), then \(9\alpha^2\) is equal to ________.JEE Mains 2026 Hard
- The value of \(\cos \,\frac{\pi }{{{2^2}}}.\cos \,\frac{\pi }{{{2^3}}}{._{..................}}.\cos \,\frac{\pi }{{{2^{10}}}}.\,\sin \,\frac{\pi }{{{2^{10}}}}\) isJEE Mains 2019 Hard
- If \(\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}\), where C is the constant of integration, then \(g\left(\frac{1}{2}\right)\) equals :JEE Mains 2025 Hard
More PYQs from JEE Mains
- Let \(y=f(x)\) be the solution of the differential equation \(y(x+1) d x-x^2 d y=0, y(1)=e\). Then \(\lim _{x \rightarrow 0^{+}} f(x)\) is equal toJEE Mains 2023 Hard
- If \(I=\int\limits_{1}^{2} \frac{d x}{\sqrt{2 x^{3}-9 x^{2}+12 x+4}},\) thenJEE Mains 2020 Hard
- \(\frac{6}{3^{26}}+\frac{10 \cdot 1}{3^{25}}+\frac{10 \cdot 2}{3^{24}}+\frac{10 \cdot 2^2}{3^{23}}+\ldots+\frac{10 \cdot 2^{24}}{3}\) is equal toJEE Mains 2026 Easy
- If \((2,3,9),(5,2,1),(1, \lambda, 8)\) and \((\lambda, 2,3)\) are coplanar, then the product of all possible values of \(\lambda\) is.JEE Mains 2022 Hard
- The area enclosed by the curves \(y^2+4 x=4\) and \(y-2 x=2\) is :JEE Mains 2023 Medium
- \(f(x)=\left\{\begin{array}{cc}\frac{\sin (x-[x])}{x-[x]} & , \quad x \in(-2,-1) \\ \max \{2 x, 3[|x|]\} & , \quad|x|<1 \\ 1 & , \quad \text { otherwise }\end{array}\right.\) where \([t]\) denotes greatest integer \(\leq t\). If \(m\) is the number of points where \(f\) is not continuous and \(n\) is the number of points where \(f\) is not differentiable, then the ordered pair \(( m , n )\) isJEE Mains 2022 Hard