Recently Active Co Ordinate Geometry Questions

let ABCD be a quadilateral with area 18 ,with side AB parallel to CD and AB=2CD.let AD be perpendicular to AB and CD.if a circle is drawn inside the quadilateral ABCD touching all the sides, then its radius is ...

The least dist. b/n y2=4ax and (y-ba)2=-4ax is 8√5a,where b is posiive. The value of b is_? ...

A silly question indeed... just started reading vectors and i got confused.. Got the full solution but am not satisfied... :( suppose (a-b)=cx(λ1a+λ2b)...................................(i) then what should be condition ...

Let S be the set of all vertices of a unit cube.Let T be the set of the triangles having vertices in S then the number of equilateral , scalene, and isoceles triangles are ? PLz answer quickly i want to check my answers.. ...

Find the locus of the foot of the perpendicular drawn from the point (0,-c) and c>0 to the normals to the parabola x2=4ay. Find the locus of midpoint of chord of the parabola y2=4ax such that normals at their extre ...

two circles with radii r1 and r2, r1>r2≥2,touch each othere externally.Find angle between direct common tangents........... ...

find teh coordinates of point from which the tangents are drawn to teh circle x2+y2-6x-4y+3=0 such that the mid pt of chord of contact is (1,1) ...

show that orthocentre of triangle formed by lines ax2+2hxy+by2=0 and lx+my+n=1 is given by x/l =y/m =(a+b)/(am2-2lmh+bl2) ...

Show that the area of triangle formed by tangents from the point (4,3) to teh circle x2+y2=9 and teh line segment joining teh points of contact is 192/25 sq units ...

prove that the tangents to circle x2+y2=5 at the pt (1,-2) also touches x2 +y2 -8x +6y +20=0 and find pt of contact. ...

Two parabola's y2=4a(x-λ1) and x2=4a(y-λ2) always touch each other, λ1 and λ2 being variable parameters. Then their points of contact lie on a _ 1) straight line 2) parabola c) circle d) hyperbola ...

Prove that the circles x2+y2+2ux+2vy=0 and x2+y2+2u1x+2v1y=0 touch each otehre if u1v=uv1 ...

The equation of bisector of internal angleA of the triangle ABC The equation of whose sides are AB:x+y=1 BC:7X-Y=15AND AC:x-y=1 ...

if eqn 2hxy +2gx+2fy+c=0 represents 2 st. lines show that they form a rectangle of area mod(fg)/h2 with axes ...

prove that lines a2x2+2h(a+b)xy+b2y2=0re equally inclined to the lines ax2+2hxy+by2=0 ...

ABC is a right angeled isoceles triangle with B=90° .it slides in the X-Y plane with its vertex A on the Y axis and with the vertex C on the X axis and such that the origin and the vertex are at the opposite side of AC.f ...

A variable st. line cuts off from the given st. lines concurrent at origin,intercepts ,the sum of reciprocals of which is a non zero constant K.Show that varibale line passes through a fixed pt. whose coordinates are (i=1 ...

if the lines ax+2y+!=0,bx+3y+!=0 and cx+4y+1=0 passes through the same point then a,b,c are in___________ ...

The lines represented by x2+2@xy +2y2=0 and the lines represented by (1+@)x2-8xy+y2=0 are equally incline then calculate prove that @=±2 ...

In the eqn. ,y-m1x-c1+K(y-m2x-c2)=0;K is a variable qty. which may have any value then the st. line represented by this eqn. passes through the pt. _________ ...

The family of lines is given as a(3x+4y+6)+b(x+y+2)=0.The line of the family situated at the greatest distance from the point P(2,3) has the equation____ ...

if ax3+by2+cx2y+dxy2=0 represents 3 distinct straight lines,so that each line is angle bisector of of the other two,then prove that c+3b=0 ...

The incenter of traingle formed by lines x=0,y=0,5x+12y=0 is______ ...

Q1if a,b,c are the three terms of AP then prove that the line ax+by+c=0 always passes through a fixed point. Q2if a,b,c are the three terms of GP then prove that the line ax+by+c=0 always forms a triangle with axes of ...

If orthocentre of triangle ABC is (4,3),centroid is (6,5) and A is (0,3),then vertices of B can be..... ...

BC is latus rectum of a parabola y2=4ax and A is its vertex , then minimum length of projection of BC on a tangent drawn in the portion BAC is ...

the st lines 12x-5y-17=0 and 24x-10y+44=0 are tangents to the same circle.Then the radius of circle is ?? ...

the common chord of a circle with centre (-4,0) and a parabola y2=8x subtends an angle 90 at the vertex.Find the radius of the circle. ...

Two parabolas y2=4a (x-lambda1) and x2=4a (x-lambda2) always touch each other(lambda1,lambda2 being variable parametres). then their point of contact lies on a ...

The angle between tangent drawn from the point (3,4) to the parabola y2 -2y+4x=0 is ...