JEE Mains · Maths · STD 12 - 8. Application and integration
A line passing through the point \(\mathrm{A}(-2,0)\), touches the parabola \(P: y^2=x-2\) at the point \(B\) in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-
- A \(\frac{7}{3}\)
- B \(2\)
- C \(\frac{8}{3}\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
Tangent \(\begin{aligned} & y=m(x+2) \\ & y^2=x-2 \\ & (m(n+2))^2=n-2 \\ & m^2 x^2+\left(4 m^2-1\right) x+\left(4 m^2+2\right)=0 \\ & D=0 \\ & \left(4 m^2-1\right)^2-4 m^2\left(4 m^2+2\right)=0 \\ & m=\frac{1}{4} \\ & y=\frac{1}{4}(n+2) \end{aligned}\) and point of tangency…
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 locus of the mid-points of the perpendiculars drawn from points on the line, \(\mathrm{x}=2 \mathrm{y}\) to the line \(\mathrm{x}=\mathrm{y}\) isJEE Mains 2020 Hard
- If for \(a >0,\) the feet of perpendiculars from the points \(A ( a ,-2 a , 3)\) and \(B (0,4,5)\) on the plane \(l x+m y+n z=0\) are points \(C(0,-a,-1)\) and \(D\) respectively, then the length of line segment \(CD\) is equal toJEE Mains 2021 Hard
- Let the mean and the standard deviation of the probability distribution
be \(\mu\) and \(\sigma\), respectively. If \(\sigma-\mu=2\), then \(\sigma+\mu\) is equal to ...........\(X\) \(\alpha\) \(1\) \(0\) \(-3\) \(P(X)\) \(\frac{1}{3}\) \(K\) \(\frac{1}{6}\) \(\frac{1}{4}\) JEE Mains 2024 Hard - If the tangent to the curve \(y=x+\sin y\) at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right),\) thenJEE Mains 2020 Medium
- If \(\mathrm{p}\) and \(\mathrm{q}\) are the lengths of the perpendiculars from the origin on the lines, \(x \operatorname{cosec} \alpha-y \sec \alpha=\operatorname{kcot} 2 \alpha\) and \(x \sin \alpha+y \cos \alpha=k \sin 2 \alpha\) respectively, then \(\mathrm{k}^{2}\) is equal to :JEE Mains 2021 Hard
- \(\lim _{n \rightarrow \infty}\left(\frac{n^{2}}{\left(n^{2}+1\right)(n+1)}+\frac{n^{2}}{\left(n^{2}+4\right)(n+2)}+\frac{n^{2}}{\left(n^{2}+9\right)(n+3)}+\ldots+\frac{n^{2}}{\left(n^{2}+n^{2}\right)(n+n)}\right)\) is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- If the circles \((x+1)^2+(y+2)^2=r^2\) and \(x^2+y^2-4 x-4 y+4=0\) intersect at exactly two distinct points, thenJEE Mains 2024 Medium
- Let \(P\) be the plane, which contains the line of intersection of the planes, \(x + y + z - 6 = 0\) and \(2x + 3y + z + 5 = 0\) and it is perpendicular to the \(xy -\) plane. Then the distance of the point \((0, 0, 256)\) from \(P\) is equal toJEE Mains 2019 Hard
- The equations of the sides \(A B, B C \& C A\) of a triangle \(A B C\) are \(2 x+y=0, x+p y=21 a(a \neq 0)\) and \(x-y=3\) respectively. Let \(P(2, a)\) be the centroid of the triangle \(A B C\), then \((B C)^2\) is equal toJEE Mains 2023 Medium
- Let the sum of the first three terms of an \(A. P,\) be \(39\) and the sum of its last four terms be \(178.\) If the first term of this \(A.P.\) is \(10,\) then the median of the \(A.P.\) isJEE Mains 2015 Hard
- Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R\) and \(a , b \neq 0)\) If the system of equations (in, \(u,v,w\)) given by \(\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0\) \(\gamma u +\alpha v +\beta w =0\) has non-trivial solution, then the value of \(\frac{a^{2}}{b}\) isJEE Mains 2021 Hard
- The integral \(\int \frac{1}{\sqrt[4]{(x-1)^{3}(x+2)^{5}}} d x\) is equal to : (where \(\mathrm{C}\) is a constant of integration)JEE Mains 2021 Medium