Home
Class 12
MATHS
Consider the parabola y^2=4xdot Let A-=(...

Consider the parabola `y^2=4xdot` Let `A-=(4,-4)` and `B-=(9,6)` be two fixed points on the parabola. Let `C` be a moving point on the parabola between `Aa n dB` such that the area of the triangle `A B C` is maximum. Then the coordinates of `C` are (a) `(1/4,1)` (b) `(4,4)` (c) `(3,2/(sqrt(3)))` (d) `(3,-2sqrt(3))`

A

`(1/4,1)`

B

`(4,4)`

C

`(3,2sqrt3)`

D

`(3,-2sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|14 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise Level -1|102 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C be chosen on the on the arc AOB of the parabola where O is the origin such that the area of DeltaACB is maximum. Then the area (in sq. units) of DeltaACB is :

Let P(4,-4) and Q(9,6) be two points on the parabola, y^2=4x and let X be any point on the are POQ of this parabola, where O is the vertex of this parabola, such that the area of Delta PXQ is maximum. Then this maximum area (in square units) is (25k)/(4) . The value of k is

If A(4,-4) and B(9,6) lies on y^2=4x and a point C on arc AOB (O= origin) such that the area of triangleACB is maximum then point c is (1) (1/4,1) (2) (1,1/4) (3) (1,1/2) (4) (1/2,1)

The point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as (a) (6,-4sqrt(3)) (b) (6,4sqrt(3)) (c) (-6,-4sqrt(3)) (d) (-6,4sqrt(3))

Let (a,b) be a point on the parabola y=4x-x^(2) and is the point nearest to the point A(-1,4) Find (a+b).

Points A, B, C lie on the parabola y^2=4ax The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangle ABC and triangle PQR

The line x-y=1 intersects the parabola y^2=4x at A and B . Normals at Aa n dB intersect at Cdot If D is the point at which line C D is normal to the parabola, then the coordinates of D are (4,-4) (b) (4,4) (-4,-4) (d) none of these

Consider the parabola x^(2) +4y = 0 . Let P(a,b) be any fixed point inside the parabola and let S be the focus of the parabola. Then the minimum value at SQ +PQ as point Q moves on the parabola is (a) |1 -a| (b) |ab|+1 (c) sqrt(a^(2)+b^(2)) (d) 1-b

y^2 = 4x be the parabola and the points A(9,6), B(4,-4) lie on the parabola such that area of /_\ABC is maximum (given C lies at the arc contain origin). Find the maximum area of /_\ABC (A) 101/2 (B) 69/2 (C) 125/4 (D) 521/3

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is (a) (3,3) (b) (2,2) (c) (6,6) (d) (4,4)

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -2
  1. A 10cm long rod AB moves with its ends on two mutually perpendicular s...

    Text Solution

    |

  2. The rate of change of volume of a sphere is equal to the rate of cha...

    Text Solution

    |

  3. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  4. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) , where c1a n dc2 are variable,...

    Text Solution

    |

  5. If 9-x^2>|x-a | has atleast one negative solution, where a in R the...

    Text Solution

    |

  6. f(x)=int0^x(e^t-1)(t-1)(sint-cost)sin t dt ,AAx in (-pi/2, 2pi), the...

    Text Solution

    |

  7. l1 and l2 are the side lengths of two variable squares S1, and S2, re...

    Text Solution

    |

  8. If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) increase in (0,oo) ...

    Text Solution

    |

  9. Let f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  10. If are positive integers, maximum value of x^(m) (a-x)^(n)" in (0,a)...

    Text Solution

    |

  11. The maximum value of (sin x)^((sin x)) is

    Text Solution

    |

  12. A helicopter flying along the path y=7+x^((3)/(2)), A soldier standint...

    Text Solution

    |

  13. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

    Text Solution

    |

  14. The largest term in the sequence an=(n^2)/(n^3+200) is given by (529)/...

    Text Solution

    |

  15. The least value of f (x) =x^3/3-abx occurs at x=

    Text Solution

    |

  16. For the curve defined as y=cosec^(-1)((1+x^2)/(2x))+sec^(-1)((1+x^2)/(...

    Text Solution

    |

  17. If f(x)=max{x^(2)-4,|x-2|,|x-4|} then:

    Text Solution

    |

  18. Given that f (x) is a non-constant linear function. Then the curves :

    Text Solution

    |

  19. If a curve with equation of the form y=ax^(4)+bx^(3)+cx+d has zero gra...

    Text Solution

    |

  20. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |