Home
Class 12
MATHS
Through point P(-1,4), two perpendicular...

Through point `P(-1,4)`, two perpendicular lines are drawn which intersect x-axis at Q and R. find the locus of incentre of `Delta PQR`.

A

`x^2+y^2+2x-8y-17=0`

B

`x^2-y^2 +2x-8y+17=0`

C

`x^2+y^2-2x-8y-17=0`

D

`x^2-y^2+8x-2y-17=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Let I(h,k) be incentre.
Incentre is equidistant from all sides. By geometry, `IP=ksqrt2`

`therefore sqrt((h+1)^1+(k-4)^2)=ksqrt2`
`therefore h^2+1+2h+k^2+16-8k=2k^2`
`therefore h^2-k^2+2h-8k+17=0`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Multiple correct|13 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Linked|10 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

A variable straight line passes through the point of intersection of the staright lines x/a+y/b=1 and x/b+y/a=1 and intersects the axes at P and Q.Find the locus of mid-point of Pq.

A striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The straight line PQ is perpendicular to AB and intersect the x and y-axes at P adn Q respectively. Find the eqution to the locus of the point of intersection of the line AQ and BP.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of DeltaPQR is double the perimeter of DeltaABC.

A variable straight line passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 and intersects the axes at P and Q. Find the locus of midpoint of PQ.

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

A straight line is drawn through the point P(2,3) and is inclined at an angle of 30^@ with the x-axis . Find the coordinates of two points on it at a distance 4 from point P.

The two circles with centre X and Y intersect each other at the points A and B, A joined with the mid -point S of XY and the perpendicular on SA through the point A is drawn which intersect the two circles at the point P and Q .Prove that PA = AQ.

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

CENGAGE PUBLICATION-COORDINATE SYSYEM -Exercises
  1. Point A and B are in the first quadrant,point O is the origin. If the ...

    Text Solution

    |

  2. Let a,b,c be in A.P and x,y,z be in G.P.. Then the points (a,x),(b,y) ...

    Text Solution

    |

  3. If sum(i=1)^4(x1^2+y 1^2)lt=2x1x3+2x2x4+2y2y3+2y1y4, the points (x1, y...

    Text Solution

    |

  4. The vertices A and D of square A B C D lie on the positive sides of x-...

    Text Solution

    |

  5. Through the point P(alpha,beta) , where alphabeta>0, the straight line...

    Text Solution

    |

  6. The locus of the moving point whose coordinates are given by (e^t-e^(-...

    Text Solution

    |

  7. The locus of a point reprersented by x=a/2((t+1)/t),y=a/2((t-1)/t) , w...

    Text Solution

    |

  8. Vertices of a variable triangle are A(3,4),B(5costheta, 5sintheta) and...

    Text Solution

    |

  9. Vertices of a variable triangle are A(3,4),B(5costheta, 5sintheta) and...

    Text Solution

    |

  10. From a point, P perpendicular PM and PN are drawn to x and y axis, res...

    Text Solution

    |

  11. The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) ...

    Text Solution

    |

  12. If the roots of the equation (x(1)^(2)-a^2)m^2-2x1y1m+y(1)^(2)+b^2=0...

    Text Solution

    |

  13. Through point P(-1,4), two perpendicular lines are drawn which interse...

    Text Solution

    |

  14. The number of integral points (x,y) (i.e, x and y both are integers) w...

    Text Solution

    |

  15. The foot of the perpendicular on the line 3x+y=lambda drawn from the o...

    Text Solution

    |

  16. The image of P(a,b) on the line y=-x is Q and the image of Q on the li...

    Text Solution

    |

  17. If the equation of the locus of a point equidistant from the points (a...

    Text Solution

    |

  18. Consider three lines as follows. L1:5x-y+4=0 L2:3x-y+5=0 L3: x+y+8=0...

    Text Solution

    |

  19. Consider a point A(m,n) , where m and n are positve intergers. B is th...

    Text Solution

    |

  20. In the given figure, OABC is a rectangle. Slope of OB is

    Text Solution

    |