JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The tangents at the point \(A (1,3)\) and \(B (1,-1)\) on the parabola \(y ^{2}-2 x -2 y =1\) meet at the point \(P\). Then the area (in unit \({ }^{2}\) ) of the triangle \(PAB\) is :-
- A \(4\)
- B \(6\)
- C \(7\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
Given curve : \(y^{2}-2 x-2 y=1\). Can be written as \((y-1)^{2}=2(x+1)\) Can be plotted as shown in figure Tangent at \(A: 2 y-x-5=0\) \({using\,T=0}\) Intersection with \(y=1\) is \(x=-3\) Hence, point \(P\) is \((-3,1)\) Taking advantage of symmetry Area of…
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 number of distinct real roots of the equation \(|\mathrm{x}||\mathrm{x}+2|-5|\mathrm{x}+1|-1=0\) is ....................JEE Mains 2024 Hard
- If \(f\left( x \right) = \left[ x \right] - \left[ {\frac{x}{4}} \right],\,x \in R\) , where \([x]\) denotes the greatest integer function, thenJEE Mains 2019 Hard
- An ordered pair \((\alpha , \beta )\) for which the system of linear equations \(\left( {1 + \alpha } \right)x + \beta y + z = 2\) ; \(\alpha x + \left( {1 + \beta } \right)y + z = 3\) ; \(\alpha x + \beta y + 2z = 2\) has a unique solution, isJEE Mains 2019 Hard
- The integral \(\int \limits_{0}^{2} \| x-1|-x| d x\) is equal toJEE Mains 2020 Hard
- \(\lim \limits_{x \rightarrow \frac{1}{\sqrt{2}}} \frac{\sin \left(\cos ^{-1} x\right)-x}{1-\tan \left(\cos ^{-1} x\right)}\) is equal toJEE Mains 2022 Hard
- Two tangents are drawn from the point \(\mathrm{P}(-1,1)\) to the circle \(\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-6 \mathrm{y}+6=0\). If these tangents touch the circle at points \(A\) and \(B\), and if \(D\) is a point on the circle such that length of the segments \(A B\) and \(A D\) are equal, then the area of the triangle \(A B D\) is eqaul to:JEE Mains 2021 Medium
More PYQs from JEE Mains
- Let \(f:(0,2) \rightarrow R\) be defined as \(f( x )=\log _{2}\left(1+\tan \left(\frac{\pi x }{4}\right)\right)\) Then, \(\lim _{n \rightarrow \infty} \frac{2}{n}\left(f\left(\frac{1}{n}\right)+f\left(\frac{2}{n}\right)+\ldots+f(1)\right)\) is equal toJEE Mains 2021 Hard
- Given that the slope of the tangent to a curve \(y = y(x)\) at any point \((x, y)\) is \(\frac{{2y}}{{{x^2}}}\). If the curve passes through the centre of the circle \(x^2 + y^2 - 2x - 2y = 0\), then its equation isJEE Mains 2019 Hard
- \(\int {\frac{{2x + 5}}{{\sqrt {7 - 6x - {x^2}} }}dx} = A\sqrt {7 - 6x - {x^2}} + B\,{\sin ^{ - 1}}\left( {\frac{{x + 3}}{4}} \right) + C\) (where \(C\) is a constant of integration), then the ordered pair \((A, B)\) is equal toJEE Mains 2018 Hard
- If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :JEE Mains 2025 Medium
- Let PQ and MN be two straight lines touching the circle \( x^{2}+y^{2}-4x-6y-3=0 \) at the points A and B respectively. Let O be the centre of the circle and \( \angle AOB=\pi/3. \) Then the locus of the point of intersection of the lines PQ and MN is:JEE Mains 2026 Hard
- If \(m\) and \(M\) are the minimum and the maximum values of \(4 + \frac{1}{2}\,{\sin ^2}\,2x - 2\,{\cos ^4}\,x\,,x\, \in R,\) then \(M - m\) is equal toJEE Mains 2016 Hard