Recently Active Co Ordinate Geometry Questions

1) A ray of light is coming along the line y = b from the positive direction of x axis and strikes a concave mirror whose intersection with xy plane is a parabola y2 = 4ax . If a and b are positive, then the equation of the r ...

C1 andC2 aretwo concentric circles the radius of C2 being twice of C1 from a point P on C2, tangents PA andPB are drawn to C1. Prove that the centroid of the triangle PAB lies on C1 ...

Let C1 and C2 be two cirlces with C2 lying inside C1. A circle C lying inside C1touces C1 internally and C2 externally. Identify the locus of the center of C ...

Let T1, T2 be two tangents drawn from (-2,0) oneo the circle C:x2+y2=1. Determine thecircles touching C and having T1, T2 as their pair of tangents. Further, find the equations of all possible common tangents to these circles ...

Is there any quick method of finding if 4 given pts are concyclic or not? (finding the eqn of the circle thru 3 pts and then checking the 4th pt in the eqn is really looooooooooong) ...

Line L has intercepts a and b on the axes,the axes are rotated thru a certain angle,now the intercepts are p and q , then A)a2+b2 = p2+q2 B)1/a2 + 1/b2 = 1/p2 + 1/q2 C)a2+p2 = b2+q2 D)1/a2 + 1/p2 = 1/b2 + 1/q2 ...

In a \Delta OAB , E is the mid pt of OB , D is such that AD:DB = 2:1 if OD,AE intersect at P ,find OP:PD @priyam,corrected the question,D is a pt on AB ...

A variable line with -ve slope passes thru \left(8,2 \right) with intercepts on the axes being P and Q , find min(P+Q) ...

Two planes P1 and P2 pass through origin. Two lines L1 and L2 also passing through origin are such that L1 lies on P1 but not on P2, L2 lies on P2 but not on P1. A,B< C are three points other than origin, then prove that t ...

T is a parallelopipe in which A, B, C ,and D are the vertices of one face. And the face just above it has corresponding vertices A`, B`, C`, D`. T is now compressed to S with face ABCD remaining same and A`, B`, C`, D` shifte ...

\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} and \frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} intersect find the vlaue of k! ...

Value of K such that \frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2} lies in the plane 2x-4y+z=7 is ...

Given are two curves x2/a2 +y2/63 =1 and y2=4x The maximum integral value of a for which there is only one common normal to the two curves is: A. 7 B. 8 C. 9 D. 10 pls help!! ...

evaluate a,b,c,d if lim x→∞ (√x4+ax3+3x2+bx+2)-(√x4+2x3-cx2+3x-d=4 ...

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Let P be a point on the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ,in the first or second quadrants,if the foci are S1 and S2,what is the minimum circum radius of \Delta PS_{1}S_{2} ? A) ae B) be C) ae/b D) ae2/b ...

if D,E,F are the feet of the perpendiculars from vertices A,B,C to opp sides,and the semiperimeter of ΔDEF = inradius of ΔABC then cosA/2cosB/2cosC/2 = ? ...

Locus of intersection of perpendicular tangents to the curve 4y3 = 27x2 ...

If θ1 and θ2 be the angles which the lines (x2+y2)(cos2 θ sin2α+ sin2θ)= (x tanθ - y sinθ)2 make with the x axis and θ= π/6 , then what is the value of (tan θ1+ tan θ2) ? answer:(-8/3 cosec 2α) ...

question below ... ...

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Find the distance between the point P(6, 5, 9) and the plane determined by the points A (3, – 1, 2), B (5, 2, 4) and C(– 1, – 1, 6). ...

Paragraph for comprehension 7 to 9 The tangents at P and P’ on the parabola y^2 = 4ax meet in T. S is the focus, O is the vertex and SP, ST and SP’ are equal to , and respectively. The tangent at the point P(x1, y1) to th ...

A line passing through A(2,2,4) and parallel to line L ≡(x-2)=(y-1)=(z-2)/3 is incident of the mirror plane x+2y+2z-5=0. The equation of the reflected ray is a) (x-1)=(y-1)/3=(1-z) b) (x-1)=(y-1)/-3=(z-1) c) x=(2-y)=z d) x= ...

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Find the condition so that the line px + qy = r intersects the ellipse x2/a2 + y2/b2 =1 in points whose eccentric anles differ by π / 4 ...

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find the length of the common chord of two circles: (x-a)2+(y-b)2=c2 and (x-b)2+(y-a)2 a) 4c2-2(a-b)2 b) 4b2-2(a-c)2 c) 2c2-2(a-b)2 d) 2c2-2(c-b)2 ...

statement 1: there exists a convex hexagon in the plane such that its sides are 1,2,3,4,5,6 units in order because Statement 2: construct an equilateral triangle of side length 9 units and remove the 3 corners of equilateral ...

Find the lengths of diagonals of the parallelogram constructed on the vectors p=2a+b and q=a-2b, where a and b are unit vectors and forming an angle of 60°. ...