Home
Class 11
MATHS
Let S be the focus of y^2=4x and a poi...

Let `S` be the focus of `y^2=4x` and a point `P` be moving on the curve such that its abscissa is increasing at the rate of 4 units/s. Then the rate of increase of the projection of `S P` on `x+y=1` when `P` is at (4, 4) is (a)`sqrt(2)` (b) `-1` (c) `-sqrt(2)` (d) `-3/(sqrt(2))`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

A point is in motion along a hyperbola y=(10)/(x) so that its abscissa increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate, when the point passes through (5,2)

Find the coordinates of the position of a particle moving along the parabola y^(2) = 4x at which the rate of increase of the abscissa is twice the rate of increase of the ordinate.

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

If the side of an equilateral triangle increases at the rate of sqrt(3) cm/s and its area at the rate of 12 cm^(2) /s, find the side of the triangle .

Let S is the focus of the parabola y^2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.

A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ in the first quadrant such that 1/(A P)+1/(A Q) sqrt(3) (b) sqrt(2) (d) >1/(sqrt(3))

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

The largest value of a for which the circle x^2+y^2=a^2 falls totally in the interior of the parabola y^2=4(x+4) is 4sqrt(3) (b) 4 (c) 4(sqrt(6))/7 (d) 2sqrt(3)

If A and B are foci of ellipse (x-2y+3)^(2)+(8x +4y +4)^(2) =20 and P is any point on it, then PA +PB = (a) 2 (b) 4 (c) sqrt(2) (d) 2sqrt(2)

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (a) (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

    Text Solution

    |

  2. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

    Text Solution

    |

  3. Let S be the focus of y^2=4x and a point P be moving on the curve s...

    Text Solution

    |

  4. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...

    Text Solution

    |

  5. If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...

    Text Solution

    |

  6. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

    Text Solution

    |

  7. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

    Text Solution

    |

  8. Parabolas y^(2)=4a(x-c(1))andx^(2)=4a(y-c(2)), where c(1) and c(2) are...

    Text Solution

    |

  9. A circle touches the x-axis and also touches the circle with centre (0...

    Text Solution

    |

  10. The locus of the vertex of the family of parabolas y=(a^(3)x^(2))/(3...

    Text Solution

    |

  11. Let C(1)andC(2) be, respectively, the parabola x^(2)=y-1andy^(2)=x-1. ...

    Text Solution

    |

  12. If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then ...

    Text Solution

    |

  13. The locus of a point on the variable parabola y^2=4a x , whose distanc...

    Text Solution

    |

  14. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

    Text Solution

    |

  15. The angle between the tangents drawn from the point (1,4) to the para...

    Text Solution

    |

  16. Statement 1: There are no common tangents between the circle x^2+y^2...

    Text Solution

    |

  17. If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then ...

    Text Solution

    |

  18. C (0,1) is the centre of the circle with radius unity. P is the parabo...

    Text Solution

    |

  19. The set of points on the axis of the parabola (x-1)^(2)=8(y+2) from wh...

    Text Solution

    |

  20. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

    Text Solution

    |