Recently Active Co Ordinate Geometry Questions

Prove that from a point (a,b) of the circle x(x-a) + y(y-b) = 0, two chords, each bisected by the axis of x (rather x-axis), can be drawn if a2>8b2 [This is not my doubt, so provide complete solution for everyone's benefit ...

a similar question to this one was asked way back........... has high chance of getting repeated....... paragraph: for each positive real no. k, let Ck denoite the circle with center at origin and radius k units.On a circle C ...

A ray represented by a unit vector u ,is reflected by a plane mirror,whose normal is given by another unit vector v,the reflected ray is along unit vector w. Express w in terms of v,u ...

(ST)2 = SP.SQ WER S = FOCUS P,Q ARE points on the parabola T = point of intwersectn of tangents at P and Q ...

find locus of center of circle which touches (y-1)2+x2=1 externally and also touches X axis. ...

The asymptotes of a hyperbola are x^2+4xy+y^2-2x+2y-2=0 and the hyperbola passes through (1,1) The centre of the hyperbola is? The conjugate axis of the hyperbola is? What is the eccentricity of the hyperbola? ...

find the maximum area of a rectangle whose two sides x=x0,x=Î -x0,which is inscribed in region bounded by y= sin x and x axis,is obtained when x0 belongds to a)(Î /4,Î /3) b()Î /6,Î /4) c)(0,Î /6) d)none ...

A.B=0 ; A.X = c,c≠0,A x X = B find X ...

The line 6x+8y=48 intersects the coordinate axes at A and B respectively. A line L bisects the area and the perimeter of the triangle OAB where O is the origin. Find the slope of this line. Options are: (a) \frac{10+5\sqrt{3} ...

from a point (sinθ,cosθ)if three normals are drawn to the parabola y2=4ax,then the value of a is: a)(1/2,1) b)[-1/2,0] c)[1/2,1] d)none ...

the sides of a triangle touch a circle x2 + y2 = a2 and 2 of the vertices are on the line |y|=b. find the locus of the third side............ ...

Let a and b be 2 non collinear unit vectors . u=a-(a.b)b and v = a x b,then |v| = ? (in terms of u , a,b) ...

WATS DA SHORTEST WAY to find da circumcenter and INCENTRE of a triangle if the 3 vertices are known? How bout ORTHO-Center?? ...

if \Theta is the angle subtended at P(0,2) by the circle 4x2+4y2-4x-12y+9=0 then a)tan \Theta /2=1/2 b)tan \Theta =4/3 c) \Theta =90 d) \Theta =45 ...

The straight line whose equation is ax+by=1 where ab>0passes through (3,4) and makes a triangle of area S with the co-ordinate axis. then the least value of S is a)12 b)24 c)6 d)7 ...

find the centre and the radius of the smaller of the two circles that touch the parabola 75y2=64(5x-3) at (6/5,8/5) and the x-axis plzzzz explain ...

Now can sum1 figure out 4 me Wer does this genral form cumk frm?? Read 14, 15 together..... *Image* *Image* ...

let S1, S2......... be the squares such that for each n≥1, the length of a side of Sn equals the length of a diagonal of sn+1. if the length of a side of S1 is 10cm, then for which of the following values of n is the area o ...

If CF is the perpendicular from the centre C of the ellipse (x2/49)+(y2/25)=1 on the tangent at any point P, and G is the point where the normal at P meets the minor axis, then what is the value 0f (CF*PG)2 ?????? ...

Normals are drawn from the pt P with slopes m_1,m_2,m_3 to the parabola y^2=4x .If Locus of P is a part of the parabola with m_1m_2 = \alpha , find \alpha ...

A circle with radius a and centre on y - axis slides along it and a variable line through (a,0) cuts the circle at points P and Q. What is the region in which the pt of intersection of tangents to the circle at points P and Q ...

An ellipse given by x^2+4y^2=16 has a circle inscribed with centre at (1,0) ,what is the maximum possible radius? Ans: \sqrt{\frac{11}{3}} ...

The foot of the perpendicular on the line 5x+y=k drawn from the origin is M the line cuts the co-ordinate axes at A and B respectively then BM:MA is a)5:1 b)15:1 c)25:1 d)2:1 ...

All chords of the curve 3x2-y2-2x+4y=0 which subtend a right angle at origin pass through a)(1,2) b)(1,-2) c)(2,1) d)(1,1) ...

If the greatest value of the term independent of x in expansion of (xsinp + x-1cosp)10 is achieved at P=θ... then the locus of point from which pair of tangents be drawn to x2+y2=4 including an angle θ is A) x2+y2= 4(4+2√ ...

Let ABCD be a square of side of length 2 units . C2 is the circle through vertices A,B,C,D and C1 is the circle touching all the sides of the square ABCD . L is a line through A then 1) If P is a point on C1 And Q is another ...

if x+Ay=1 and x=a(≠1) are the equations of the hypotenuse and a side of a right angled isosceles triangle then the value of A is a)+1 or-1 b)+aor-a c)+1/a or -1/a d)+2or-2 ...

If inside a big circle exactly 24 small circles each of radius 2 can be drawn in such a way that each small circle touches the big circle and also touch both its adjacent small circles. Then the radius of the big circle is... ...

Let 2x^2+y^2-3xy=0 be the eqn of a pair of tangents from the origin to a circle of radius 3 ,with centre in first quadrant,find the distance from O to the pt of contacts ...

For the circle x^2+y^2=r^2 ,find value of r for which area enclosed by tangents from P(6,8) and its chord of contact is maximum ANS : 5 units ...