Home
Class 12
MATHS
The straight line ax+by=1 intersect the ...

The straight line `ax+by=1` intersect the circle `x^(2)+y^(2)=c^(2)` at P and Q , if the chord `bar PQ` substends and angle `45^(@)` at the centre of the circle, show that `c^(2)(a^(2)+b^(2))=2(2-sqrt(2))`.

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise CALCULUS|84 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

The straight line y=mx+c cuts the circle x^2+y^2=a^2 at real points if

If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = 25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^2 + y^2 = 25 .

The condition that the chord xcos alpha +ysin alpha -p=0 of x^2+y^2-a^2=0 may subtend a right angle at the centre of the circle is

If the chord y = mx + 1 subtends an angle of measure 45^0 at the major segment of the circle x^2+y^2=1 then value of 'm' is

The line x =2 y intersects the ellipse (x^(2))/(4) +y^(2) = 1 at the points P and Q . The equation of the circle with pq as diameter is _

The locus of the mid-points of the chords of the circle x^(2)+y^(2)+2x-2y-2=0 which make an angle of 90^(@) at the centre is

The pole of a straight line with respect to the circle x^2+y^2=a^2 lies on the circle x^2+y^2=9a^2 . If the straight line touches the circle x^2+y^2=r^2 , then :

The intercept on the line y = x by the circle x^2 + y^2 - 2x = 0 is bar(AB) Equation of the circle on bar(AB) as a

The eccentric angles of the two points P and Q on the ellipse x^2/a^2+y^2/b^2=1(a>b) are theta and phi resp.If the chord PQ makes angle 90^@ with the vertex (a,0)of the ellipse then show that tan(theta/2)tan(phi/2)=-b^2/a^2

If the circle C_(2) of radius 5 intersects othe circle C_(1):x^(2)+y^(2)=16 such that the common chord is in maximum length and its slope is (3)/(4) , then the centre of C_(2) will be-

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Prove that the area of the triangle with vertices (p,q),(x(1),y(1)) an...

    Text Solution

    |

  2. The base of triangle passes through a fixed point (f,g) and its other ...

    Text Solution

    |

  3. The straight line ax+by=1 intersect the circle x^(2)+y^(2)=c^(2) at P ...

    Text Solution

    |

  4. The equations of two equal sides AB and AC of an isosceles triangle AB...

    Text Solution

    |

  5. One diagonal of a square is the portion of the straight line 7x+5y=35 ...

    Text Solution

    |

  6. If the straight lines a^(2)x+ay+k=0, b^(2) x+by+k=0 and c^(2)x+cy+k=0 ...

    Text Solution

    |

  7. Show that the circle x^(2)+y^(2)-2y-15=0 lies completely within the ci...

    Text Solution

    |

  8. Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3...

    Text Solution

    |

  9. Two sides of a rhombus lyin in the first quadrant are given by 3x-4y=0...

    Text Solution

    |

  10. A line joining two points A (2,0) and B(3,1) is rotated about A in the...

    Text Solution

    |

  11. A (3,0) and B(6,0) are two fixed points and P(x(1),y(1)) is a variable...

    Text Solution

    |

  12. Find the coordinates of the centroid of the triangle, formed by the li...

    Text Solution

    |

  13. The points (1,3) and (5,1) are two oppsite vertices of a rectangle. Th...

    Text Solution

    |

  14. Show that the lines ax+by+c=0, ax-by+c=0, ax-by=c ax+ by-c=0 (a ne b) ...

    Text Solution

    |

  15. Let A(ct(1), (c)/(t(1))), B(ct(2),(c)/(t(2))) and C(ct(3),(c)/(t(3))) ...

    Text Solution

    |

  16. The circle A and B of a line segment of constant length c unit slides ...

    Text Solution

    |

  17. A variable striaght line of slope 4 intresects the hyprbola xy=1 at tw...

    Text Solution

    |

  18. If x cos alpha+ y sin alpha=p, where p=(-sin^(2) alpha)/(cos alpha) be...

    Text Solution

    |

  19. A tangent drawn from the point (4,0) to the circle x^(2)+y^(2)=8 touch...

    Text Solution

    |

  20. A(x(1) y(1)) and B(x(2), y(2)) are two given points on a circle. If th...

    Text Solution

    |