Home
Class 12
MATHS
PSQ is a focal chord of a parabola whose...

PSQ is a focal chord of a parabola whose focus is S and vertex is A. PA, QA, are produced to meet the dirrecterix in R and T. Then `/_RST` is equal to

A

`30^(@)`

B

`90^(@)`

C

`60^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Let `P-=(at_(1)^(2),2at_(1))andQ-=(at_(2)^(2),2at_(2))`.
`rArrt_(1)t_(2)=-1`
Equation of AP is `y=(2)/(t_(1))x_(1)`.
`rArrR-=(-a,-2a//t_(1))`
Similarly, `T-=(-a,(-2a)/(t_(2)))`
Slope of RS `=(((-2a)/(t_(1))))/(2a)=-(1)/(t_(2))`
Slope of TS `=(((-2a)/(t_(2))))/(2a)=-(1)/(t_(2))`
Now, `(-(1)/(t_(1)))xx(-(1)/(t_(2)))=(1)/(t_(1)t_(2))=-1`
`rArr" "angleRST=90^(@)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l_1, then find B Sdot

PQ is a chord ofthe parabola y^2=4x whose perpendicular bisector meets the axis at M and the ordinate of the midpoint PQ meets the axis at N. Then the length MN is equal to

Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 The length of the chord of parabola on the x-axis is

PQ is a normal chord of the parabola y^2 =4ax at P, A being the vertex of the parabola. Through P, a line is drawn parallel to AQ meeting the x-axis at R. Then the line length of AR is

The abscissa of the three points P , Q , R of an ellipse, one of whose focus is S , are in A.P . Prove that the focal distances of the three points are also in A.P .

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 Tangents drawn to the parabola at the extremities of the chord 3x+2y=0 intersect at angle (a) pi//6 (b) pi//3 (c) pi//2 (d) none of these

The triangle P Q R of area A is inscribed in the parabola y^2=4a x such that the vertex P lies at the vertex of the parabola and the base Q R is a focal chord. The modulus of the difference of the ordinates of the points Qa n dR is

Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as) be distinct points on the parabola y^(2)=4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0). If st=1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa n dQ , then P Q substends a right angle at the origin. Statement 2: Double ordinate equal to twice of latus rectum of a parabola subtends a right angle at the vertex. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

    Text Solution

    |

  2. Two parabola have the same focus. If their directrices are the x-and t...

    Text Solution

    |

  3. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

    Text Solution

    |

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

    Text Solution

    |

  5. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

    Text Solution

    |

  6. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

    Text Solution

    |

  7. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  8. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

  9. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  10. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) where c1 and c2 are variables, ...

    Text Solution

    |

  11. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

    Text Solution

    |

  12. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to...

    Text Solution

    |

  13. The center of the circle which cuts parabola orthogonally the parabol...

    Text Solution

    |

  14. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

    Text Solution

    |

  15. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  16. find the equation of hyperabola where foci are (0,12) and (0,-12)and t...

    Text Solution

    |

  17. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

    Text Solution

    |

  18. The straight lines joining any point P on the parabola y^2=4a x to the...

    Text Solution

    |

  19. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  20. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |