Recently Active Co Ordinate Geometry Questions

CIrcle C (r=1) touches X axis at A.Centre Q of C lies in Quad I.Tangent from origin touches C at T and P lies on it such that OAP is rt triangle (at A).perimeter =8 Q1 Find PQ Q2 eqn of circle Q3 eqn of tangent here is fig... ...

By transforming to parallel axes through a properly chosen point (h,k), prove that the eqn, 12x2-10xy+2y2+11x-5y+2=0 can be reduced to one containing only terms of the second degree. ...

Find what straight lines are represented by the following eqn: x3-6x2+11x-6=0 ...

The following eqn represents two straight lines. 6y2-xy-x2+30y+36=0 Find their point of intersection and the angle between them. ...

The equation of circle(s) of radius 1 & touching the circles x2 + y2 - 2|x| = 0 is ? ...

Find the area of the pentagon whose vertices are (4,1) (3,6) (-5,1) (-3,-3) and (-3,0) Use 1/2{ |x1 x2| + |x2 x3| +......+ |xn x1| } |y1 y2| |y2 y3| |yn y1| ...

Find the fixed point which all chords of the curve 3x2 - y2 - 2x + 4y = 0, subtending a right angle at the origin, pass through. ...

Solve this one Guys!!!!! The height of a parabolic arch is 18m.The span of the arch is 24m.Find the height of the arch 8m on each side from its central position? ...

The new coordinates of point (3,4) when it is rotated through an angle of \Pi /4 about the origin in anticlockwise direction Ans(-1/√2 , 7/√2) ...

ABC is a right angled isosceles triangle, right angled at A(2,1).If the equation of side BC is 2x+y=3, then find the combined equation of lines AB and AC. Ans-- 3x2-3y2-8xy-4x+22y-7=0 ...

If x-2y+4=0 and 2x+y-5=0 are sides of a isosceles triangle having area 10 sq. units.Find the equation of third side?(Note that its an right angled triangle) ...

Q) Let S1 and S2 be foci of an ellipse of equation : (x^2/a^2)+(y^2/b^2)=1 Locus of reflection of S1 with respect to any tangent to the ellipse is : a) circle b) parabola c) ellipse d) hyperbola ...

Find the equation of a str line equally inclined to the axes and equidistant from points (1,-2) and (3,4) ...

A triangle the lengths of whose sides are a,b&c is placed such that the mid points of its sides are on the coordinate axes , if the equation of the plane of the triangle be x/α + y/β + z/γ=1 then (A) α = 1/2 (a2+b2+c2)/2 ...

If the orthocentre of ΔABC formed by the intersection of lines 2x + 3y - 1 = 0, x + 2y - 1 = 0 & ax + by - 1 = 0 is origin, find a, b. ...

a circle is inscribed in a equilateral triangle of side a.find the area of any square inscribed in the circle. ...

FIITJEE HCT-6 Qsn..... If a central conic is represented by the std form ax^2+2hxy+by^2=0 with the condition that tangents at any point have a constant area (=k) of the triangle that they form with the co-ordinate axes, then ...

An ellipse with axes parallel to OX & OY cuts the parabola y2 = 4x at (1,-2) & touches it at (4,4) , the coordinates of the other points of intersection is (A) (9,-6) (B) (9,6) (C) (4,-4) (D) (1,-2) ...

Consider an ellipse x2/sec2a + y2/tan2 a = 1 ,0<a<pi/4 with foci S1 & S2 . Let M be a point on the y-axis such that OM = OS1 , where O is origin. Which of the following r correct? (A)M lise inside the ellipse (B) M lies ...

From a variable point P on y=x-3 tangents PQ& PR are drawn to the circle x2+y2 = 4 , Q' & R' r the corresponding points of Q & R on the ellipse x2/4+y2=1 in the same quadrants as Q & R The locus of the midpoint of Q' R' is an ...

the coordinates of othocenter of triangle A(x1,y1),B(x2,y2),C(x3,y3) is {(x1 tanA+x2 tanB+x3 tanC)/(tanA+tanB+tanC)},{(y1 tanA+y2 tanB+y3 tanC)/(tanA+tanB+tanC)} give me the proof of it. ...

Q1 if y=2x-3 is a tangent to parabola y2=4a(x- 1/3 ) then a= ?? i did this way..eqn of tangent to parabola:y=mx-m/3+a/m given that y=2x-3 is tangent Comparing gives us m=2 and proceeding we get a=-14/3 but ans is given a= 2± ...

Let PQ be a chord of the ellipse x2/a2 + y2/b2 = 1 , which subtends an angle of pi/2 radians at the centre . If L is the foot of perpendicular from (0,0) to PQ , then (A) Locus of L is an ellipse (B) locus of L is circle conc ...

If Ellipse E_n is drawn such that it touches Ellipse E_{n-1} at the extremities of the major axis, and has it's foci at the extremities of the minor axis of E_{n-1} then answer the following Qsns.... 1) Eccentricity e_n of El ...

(1) The sum of X-coordinate of the point of Intersection of the curves x^{2}=x+y+4 and y^{2}=y-15x+36 in X-Y plane. ...

A quadrilateral has sides 2,3,9....diagonals are at rt.angles. Find all possible values of the 4th side.... ...

(1) find total no. of Integral point that can be inside or on the circle x^{2}+y^{2}=49 ...

a parabloa y^2=4x is given.also family of lines 2ax+by+2c=0 is given where a,b,c are in AP Q1 waht is combined eqn of members of family of lines where tangents are to a give parabola Q2 if secants are drawn to above parabola ...

Sorry ..double post[2] ...

Sorry, the right question is:- "The sides AB & AC are bisected at right angles by the pair of straight lines y2-5xy-4x2=0. The base BC of the triangle passes through a fixed point (4,5). Here, AB, AC & BC are the sides of a t ...