Recently Active Co Ordinate Geometry Questions

‘O’ is a fixed point and ‘P’ , any point on a given circle ; OP is joined and on it a point ‘Q’ is taken so that OP . OQ = a constant quantity k ; prove that the locus of Q is a circle which becomes a straight lin ...

If by any change of axes and without change of origin, the quantity ax + 2hxy + by becomes, a'x' + 2h'x'y' + b'y' , the axes being rectangular in each case , then prove that, a + b = a' + b', and ab - h2 = a'b' - h'2 . ...

If the tangent drawn from the point (t2,2t) on the parabola y2=4x is same as the normal drawn at a point (√5 cosφ, 2sinφ) on the ellipse 4x2+5y2=20, Find the values of t and φ. ...

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

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If ellipse has major axis length 2 2 unit and the angle between the lines joining the focus to the minor axis is 90°,then calculate the length of semi latus rectum ...

One of the bisectors of the angle between lines a(x-1)2+2h(x-1)(y-1)+b(y-2)2=0 is x+2y-5=0 The other bisector is ???? ...

an ellipse has major axis and minor axis lengths as 2a , 2b let the foci be x1,y1 and x2,y2 and h,k be its center and if it slides between co-ordinate axes such that it touches the x and y axis at all times i)find the locus o ...

If the tangent from a point P to the circle x^2+y^2=1 is perpendicular to the tangent from P to the circle X^2+y^2=3.Then find the locus of P.. ...

In triangle ABC equation of side BC is x-y=0.Circumcentre and Orthocentre of the triangle are (2,3) and (5,8) respectively.Find the equation of circumcircle of the triangle.. ...

Find the Orthocentre of the triangle ABC where A=(a cos x1,a sin x1) B=(a cos x2,a sin x2) C=(a cos x3,a sin x3) ...

In ΔABC A=(1,2). Internal angle bisectors through B and C are y=x and y=-2x. Inradius of ΔABC is: A) 1/√3 B) 1/√2 C) 2/3 D) None of these ...

Try to prove that the locus of the centre of a circle that cuts two given circles orthogonally is the radical axis of the two given circles.(very important proof in coordinate geometry) ...

Let C be any circle with centre (0,√2). Prove that at the most two rational points can be there on C. (A rational point is a point both of whose coordinates are rational numbers.) (past JEE question) ...

What is a normal to a circle ???????? ...

9. A variable line, drawn through the point of intersection of the straight lines x/y + y/b = 1 & x/b + y/a =1, meets the coordinate axes in A & B. Show that the locus of the mid point of AB is the curve 2xy(a+b) = ab(x+y). 1 ...

Please explain the following.....how it's working. Suppose a curve 3x2-y2-2x+4y=0 has all chords subtending a right angle at the origin. Let equation of chord be lx+my=1 To make the equation of the curve HOMOGENEOUS 3x2-y2-2( ...

Please explain the following.....how it's working. Suppose a curve 3x2-y2-2x+4y=0 has all chords subtending a right angle at the origin. Let equation of chord be lx+my=1 To make the equation of the curve HOMOGENEOUS 3x2-y2-2( ...

find locus of center of circle which touches (y-1)2+x2=1 externally and also touches X axis. if u're getting x2=4y and x=0,think again!!! ...

{2} Find the coords of the Orthocentre of a triangle of sides x + y = 1 2x + 3y = 6 4x - y = 4 WITHOUT FINDING THE COORDS OF ITS VERTICES!!! {6}A line is such that its segment b/w the lines 5x - y - 4=0 & 3x + 4y - 4=0 is bis ...

Ques1) A triangle with sides 5,12 and 13 has both inscribed and circumscribed circles. The distance b/w the centres of these circles is (a)2 (b) 5/2 (c) 65 (d) 65/2 Ques2) Given A(0,0) , ABCD is a rhombus of side 5 units wher ...

give the necessary condition for a line y=mx + c to be normal to : 1)ellipse 2)parabola 3)hyperbola ...

Find equation of conjugate axis of hyperbola xy-3y-4x+7=0 ...

A rectangular hyperbola passes through two fixed points and its assymptotes are in given directions.prove that its vertices lie on an ellipse and hyperbola which intersect orthogonally ...

What is the minimum distance between circle x2+y2=9 and curve 2x2+10y2+6xy=1? ...

If x2+y2-14x-6y-6=0 ,then find maximum possible value of 3x+4y ...

1)AB is a chord of the circle x2+y2=25/2.P is a point such that PA=4 and PB=3.If AB=5,then the distance of P from the origin is _____ ...

http://yfrog.com/5fabcmjyj Show the equation for AB to be minimum. Please use algebra. The answer is b^1/3x +a^1/3y = a^1/3b^1/3 ( a^2/3 +b^2/3) Please show also. ...

A line of inclination 135* passes through P(3,4).Find the points on it , each of which is at a distance of 2 2 units away from P. Please Explain.Thanks. ...

If p,q are the perpendicular distances from the origin to the lines xsecα+ycosecα = a and xcosα - ysinα = acos2α respectively then show that 4p2 + q2 = a2 ...