Frequent Co Ordinate Geometry Questions

this question is from co-ordinate geometry... if the straight lines y=4-3x ; ay=x+10 ; 2y+bx+9=0 represent the three consecutive sides of a rectangle then what is the value of ab? plz show the work out as well thnx in advance ...

A parabola is drawn touching the axis of x at the origin and having its vertex at a given distance k from the axis.Prove that the axis of the parabola always touches x2=-8k(y-2k). ...

Point P(a, b) is in the first quadrant. A circle of radius r, centre P and containing points in each quadrant is drawn. If AK is the area inside the circle in the Kth quadrant, K=1, 2, 3, 4, then A1-A2+A3-A4= (a) ab (b) 2ab ( ...

Find incenter of a triangle whose sides are 7x-5y+11=0, x + y -15=0,7x+17y+65=0 obtain the equation of the circle ...

1)If α and β are ends of a focal chord of an ellipse of eccentricity e, find tan(α/2).tanβ(/2) 2)Normals drawn to ellipse x2/a2 + y2/b2 =1 at P meet the coordinate axes at A, B. Find the locus of mid point of A and B. 3)A ...

C1 and C2 be two concentric circles.The radius of C2 being twice that of C1.From a point P on C2 tangents PA and PB are drawn to C1.Prove that the centroid of the triangle PAB lies on C1. ...

If PQ is a double ordinate of the Hyperbola x2/a2 - y2/b2 = 1 such that OPQ is an equilateral triangle ,O being the centre of the hyperbola..Then the range of eccentricity 'e' of the hyperbola is???? ...

If G b the centroid of a triangle ABC n O b any other point then prove that : 1.) AB2+ BC2+ CA2 ≡ 3( GA2+ GB2+ GC2) 2.)OA 2+ OB 2+ OC 2 = GA 2+ GB 2+ GC 2+ 3GO 2 ...

Find the locus of the intersection of two normals to the ellipse x2/a2 + y2/b2=1 which are perpendicular to each other?????? ...

The minimum distance of the centre of the ellipse x2/16 + y2/9 = 1 from the chord of contact of mutually perpendicular tangents of the ellipse is????? ...

In a triangle ABC,the coordinates of the vertex A are (4,-1). If the equations of the bisectors of angles B and C are x-1=0 and x-y-1=0 respectively.Find the coordinates of B and C and the equations of the sides AB and AC. ...

Let x2/a2 + y2/b2 =1(a>b) be a given ellipse.Suppose an ellipse congruent to the given ellipse is drawn with the same centre and with the same axes such that it touches the given ellipse at the extremities of the major axi ...

Find the equation of the largest circle with centre (1,0) that can be inscribed in the ellipse x2+4y2=16. ...

The minimum are of triangle formed by any tangent to ellipse x2/a + y2/b =1 with the coordinate axes is : ...

If we want to find out the the equation of the angle bisector of one of the angles of a triangle, how do we find out which sign(+/-) to take? Sir had told this in class but I can't remember now. ...

ABC is an equilateral triangle such that the vertices B and C lie in two parallel lines at a distance 6.if A lies between the parallel lines at a distance 4 from one of them then find the length of the side of the equilateral ...

Prove that the lines joining the middle points of opposite sides of a quadrilateral and the line joining the middle points of its diagonals meet in a point and bisect one another.. ...

A,B,C,D....... are 'n' points in a plane whose coordinates are (x1,y1),(x2,y2),(x3,y3)..........AB is bisected in the point G1..G1C is divided at G2 in the ratio 1:2 ..G2D is divided at G3 in the ratio 1:3..G3E at G4 in the r ...

Which topics from S.L.Loney are not required for JEE? ...

How to find the circumference of an ellipse? ...

A line is drawn through a fixed point P (m,n) to the circle x2 + y2 = r2 at A and B. Find PA x PB. ...

find the eqn. of those tangents to the circle x2 + y2 - 2x - 4y - 4 = 0 which are parallel to the line 3x - 4y - 1 = 0 ...

A circle along with one of its diameter AB are given.There lies a point P in the plane.Construct the perpendicular to AB through P using only a ruler.(A ruler can only connect 2 points). ...

Find the locus of the centroid of an equilateral triangle inscribed in the ellipse x2/a2 + y2/b2 =1 (Ans is (a2+3b2)x2/a2 + (3a2+b2)y2/b2 =(a2-b2)2...please give the entire working) ...

Consider 6 points located at A=(0,0),B=(0,4),C=(4,0),D=(-2,-2), E=(3,3) and F=(5,5).Let R be the region consisting of all points in the plane whose distance from A is smaller than that from any other of the given points (othe ...

there is a isosceles triangle inside a parabola y2=x, with one vertex (0,0), than find the length of the sides of triangle ...

The circle x2+y2+2kx=0,k belongs to R,touches the parabola y2=4x externally.Then (a)k>0 (b)k<0 (c)k>1 (d)none of these Ans is (a). i have put y2=4x in the eq.of the circle.and in the quad.of x,i put b2=4ac.i got k=-2 ...

Can someone tell me, how is the equation of a plane passing through the line of intersection of two planes u = 0 and v = 0 given by, u + ∂v = 0 where, '∂' is a scalar quantity?? ...

Find eccentricity of the conic given by the equation y= x - 1/x ? ...

@ circles are drawn thru the pts(a,5a) and (4a,a) to touch y axis.Prove that they intersect at tan-1(40/9) ...