Recently Active Co Ordinate Geometry Questions

If the circles x2+y2+2x+2ky+6=0 and x2+y2+2ky+k=0 intersect orthogonally , then k is a)2 or -3/2 b)-2 or -3/2 c)2 or 3/2 d) -2 or 3/2 .........what is meant by "circles intersect orthogonally".Plz show with a diagram. ...

y = mx+2 will cut the pair of lines 2x2 - 3xy + y2 - x + y = 0 , at only one real point if m is equal to A) 1 B) -1 C) 2 D) -2 [multiple options correct] ...

prove that teh lines represented by ax^3+bx^2y+cxy^2+dy^3=0 will bisect teh angles between teh oder two if (3a+c)^2(bc+2cd-3ad)=(b+3d)^2(bc+2ab-3ad) dbt ...

Q1 If point moves insdie equilateral triangle of side length 3 unit such taht it is nearer to the angle bisectors of the triangle than to any sides.then calculate area traced by point P Q2 Let L1=y/b +z/c ;x=0 L2=x/a -z/c ;y= ...

The locus of the orthocentre of the triangle formed by the lines ( 1 + p )x - py + p( 1 + p ) = 0, ( 1 + q )x - qy + q( 1 + q ) = 0, and y=0 (where p not equal to q ) is A) Hyperbola B) parabola C) ellipse D) straight line ...

Find the locus of point of chord of contact of tangents from which to the ellipse x2/a2 +y2/b2=1 touches the circle x2+y2=c2 couldnt understand what question wants ??? ...

A variable st. line is drawn thru the point A(10,-8) to intersect the curve x^2-xy+y^2+4x-5y-2=0 at the points B and C. A point P is on the chord BC such that AB, AP,AC are in HP., then P moves on a) a line b) a circle C) a p ...

1) If the normal at one end of the latus rectum of an ellipse x2/a2+y2/b2=1 passes through the one end of the minor axis then A. e4-e2+1=0 B. e2-e+1=0 C. e2+e+1=0 D. e4+e2-1=0 2) In an ellipse the eccentric angle of any point ...

If (4k1,k1^2,1) and (4k2,k2^2,1) are two points lying on the plane in which 1,2,1 are mirror image to each other then k1k2 equals a) -3/2 b) -5/2 c) -7/2 d) -9/2 ...

P is a point inside or on boundary of ΔABC having perimeter p and area Δ . R is a point in the plane of ΔABC such that PR ≤5 .The area of region in which point R lies is ?? ...

The circles on focal radii of a parabola as diameter touch A The tangent at the vertex B The axis C The directrix D None of above ...

Co-ords. of centre of circle which bisects the circumferences of the circles : x2+y2 = 1 ; x2+y2+2x-3=0; x2+y2+2y-3 = 0 is : A) (-1,-1) B) (3,3) C) (-2,-2) D) (2,2) Ans : (-2,-2) ...

Prove that for any triangle inscribed in a rectangular hyperbola its orthocenter also lies on that same rect hyperbola ...

Let PQ specified by the equation x + y = 3 3 be a chord to the circle x2+y2=27. If the point R moves on the circle, then the locus of centriod of triangle PQR is a circle, the square of whose radius is - ...

From a pt perpendicular tangents are drawn to the ellipse x2+2y2=2.The chord of contact touches a circle which is concentric with the given ellipse.Find the ratio pf maximum and minimum area of circle?? ...

If the line y- 3 x+3=0 cuts the parabola y2=x+2 at A and B,then PA.PB is equal to (P≠( 3 ,0) Solution as in book (y-0)/( 3 /2)=(x- 3 )/(1/2)=r On solving with y2=x+2 3r2/4 = r/2 + 3 +2 PA.PB=|r1r2| = (4( 3 +2))/3 ...

If y1,y2 are the ordinates of the two points P and Q on the parabola and y3 is the ordinate of the point of intersection of tangents at P and Q,then y1,y2,y3 are in AP.Prove ...

Q1 If length of major axis intercepted between tangent and normal at a point (acosθ ,bsinθ ) on the ellipse x2/a2 +y2/b2=1 is equal to semi major axis,prove that eccentricity is (secθ (secθ -1))1/2 i am unable to reach th ...

A line intersencts hte ellipse x2/a2 +y2/b2=1 at P and Q and the parabola y2=4d(x+a) at R and S.The line segment PQ subtend right angle at the centre of ellipse.Find the locus of hte point of intersection of tangents to the p ...

If A(1,p2) , B(0,1), C(p,0) are the co-ordinates of the three points then the value of p for which the area of the triangle ABC is minimum is : A) 1/√3 B) - 1/√3 C) 1/√3 or -1/√3 D) None of these Ans: D ...

find the conjugate hyperbola of xy-2x-4y+4=0 ...

All the above questions of circles are of Bansal Class assignments. ...

In the xy plane the length of the shortest path from (0,0) to (12,16) that does not go inside the circle (x-6)2+(y-8)2=25 is : A) 10√3 B) 10√5 C) 10√3 + 5π/3 D) 10 + 5π Ans: C ...

A piece of cheese is located at (12,10) in a co-ordinate plane. A mouse is at (4,-2) and is running up the line y= -5x + 18. At the point (a,b) the mouse starts getting farther from the cheese rather than closer to it. The va ...

The locus of the mid-points of the chords of the circle x2+y2-ax-by=0 which subtend a right angle at (a/2 , b/2) is _____________ . Ans : x2+y2-ax-by+ a2+b2/8 =0 ...

a good question for jee aspirants new to this forum...... *Image* suppose an insect (without wings) has to crawl from vertex A to vertex B of the cube of side a shown in the figure then find the minimum distance that the inse ...

Ques 1) If the point (cos θ , sin θ ) does not fall in that angle between the lines y = |x-1| in which the origin lies, then θ belongs to (a) (∩ /2 . 3∩ /2) (b) (-∩/2 , ∩/2) (c) (0,∩) (d) none of these Ques 2) If ...

Two circles of unit radius have their center at (0,2) and (1,0) find the equation of their parallel common tangents. ...

If a triangle is inscribed in a rectangular hyperbola,the locus of its orthocentre is ? ...

1.ABCD is a rectangle with A(-1,2) B(3,7) and AB:BC=4:3.If distance of the origin from the centre of the rectangle is d,then find [d]. ...