Recently Active Co Ordinate Geometry Questions

\hspace{-16}$The Minimum value of the Expression \\\\\\ $\bf{\sqrt{(x_{1}-x_{2})^2+\left(\frac{x^2_{1}}{20}-\sqrt{(17-x_{2})\times (x_{2}-13)}\right)^2}}$\\\\\\ Where $\bf{x_{1}\in \mathbb{R^{+}}}$ and $\bf{x_{2}\in (13,17)}$ ...

The condition that the chord x cos A+y sin A-p=0 of x2+y2-a2=0 may subtend a right angle at the center of the circle is: (a)a2=2p2 (b)p2=2a2 (c)a=2p (d)p=2a ...

if two circles each of radius 5 unit touch each other at (1,2) and the equation of their common tangent is 4x+3y=10,then the equation of the circle, a portion of which lies in all the quadrants is: (a)x2+y2-10x-10y+25=0 (b)x2 ...

Here is a question regarding motion on an ellipse. Elliptical Motion follows Kepler’s Equation: E - e sin(E) = M E and M are angles, measured in radians, and e is a constant: 0 < e < 1. The period of motion is T. In t ...

If the equation y=1+x-2√x represents a parabola then coordinates of vertex are? Please explain how you solved it! Answer is (1/4,1/4) ...

\hspace{-16}$If $\bf{x_{1},x_{2}\in \mathbb{R}}$ and $\bf{f\big(x_{1},x_{2}\big)=\big(x_{1}-x_{2}\big)^2+\big(3\sqrt{8}+\sqrt{(4-x^2_{1})}-\sqrt{(x^2_{2}-16)}\big)^2}$\\\\ Then $\bf{f\big(x_{1},x_{2}\big)_{Min.}}$ is from ask ...

if the curves ax2+4xy+2y2+x+y+5=0 and ax2+6xy+5y2+2x+3y+8=0 intersect at 4 concyclic points then the value of |a| is ??? ...

Find the equation and length of common tangents to x^2/a^2 - y^2/b^2=1 and y^2/a^2 -x^2/b^2=1 . Please explain how you have solved it Answers: x±y=±√(a^2-b^2) And √2(a^2+b^2)/√(a^2-b^2) ...

Shan parks his car among 6 cars already standing in a row, his car not being parked at an end. on return he finds that only 4 of the 7 cars are still there. wHAT IS THE PROBABAILITY THAT BOTH THE CARS PARKED ON BOTH SIDES OF ...

The vertices of a triangle ABC lies on a rectangular hyperbola such that the orthocentre of the triangle is (3,2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axis. if the two perpendicular t ...

bisector of an angle divides the triangle into two similar triangles. True or false?. In a.s. Prakashan,it is true. In arihant,it is false. ...

Consider a triangle ABC formed by three points t1 , t2 , t3 on the parabola y2=4ax. The focus S is the orthocentre of the triangle. Calculate : (t1-1)(t2-1)(t3-1) ...

The eq x3+ax2y+bxy2+y3 represents 3 straight lines. if 2 of them r perpendicular then find the eqn of the 3rd line.. ...

x/a + y/b + z/c = 1 intersects the coordinate axes at A,B,C. if triangle PQR has mid points A,B,C then which of the following is/are true ; 1)ar(triangle PQR) = 2 √(a2b2+b2c2+c2a2) 2) foot of normal to triangle AC from O is ...

\hspace{-16}$Min. distance b/w $\mathbf{y^2=4x}$ and $\mathbf{x^2+y^2-12x+31=0}$ is ...

\hspace{-16}$Min. Area of Circle Which touches the Parabolas $\mathbf{y=x^2+1}$ and $\mathbf{x=y^2+1}$ ...

The circle x^2+(y-4)^2 = 25 intersects x-axis at points A and B . a point p lies on the major segment of the circle . the bisector of the angle APB for any point p can be given by the equation is? answer = y = mx - 1 ...

Q)The no. of rational pts(a pt is rational if both its co-ordinates are rational),on the circumference of a circle having centre (Ï€,e). (a)at most one (b)exactly one (c)exactly two (d)infinite We have to find this for variab ...

given a line with its equation ax + by + c = 0 suppose we rotate the co-ordinate axis with an angle of 78°, what will happen to the eqn. of the line? ...

Show that the perpendiculars from the centre upon all chords, which join the ends of perpendicular diameters, are of constant length in an ellipse. ...

Let P be any point on the parabola *Image* between its vertex and the positive end of the latus rectum. M is the foot of perpendicular from the focus S on the tangent at P. Then find the maximum value of AREA of *Image* ? ...

An elipse of major axis 20√3 and minor axis 20 slides along the co-ordinate axes and always remains confined in the 1st quadrant. The locus of the centre of the ellipse describes the arc of a circle. Find the length of this ...

There r exactly 2 points on the ellipse x2/a2 =+ y2/b2 =1.whose distance from the centre of the ellipse is same and equal to (1/√2 ) x (√(a2+2b2). Find the eccentricity of the elipse. ...

the eqn 8x^2 -14xy +3y^2 +10x +10y -25=0 represents adjacent sides of a ||ogram whose diagonals intersect at the points(3,2)...find the eqn of other 2 sides ,.... ...

If a triangle is formed by any 3 tangents of the parabola y2= 4ax, two of whose vertices lie on the parabola x2=4by, then find the locus of the 3rd vertex. ...

1) From a point P , Tangents are drawn are drawn to the ellipse x2/a2 + y2/b2 =1. If the chord of contact touches the ellipse x2/c2 + y2/d2 =1 tHEN FIND THE LOCUS OF P. ...

Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a stra ...

1) Inside a semi-circle of unit radius, two circle of radii r1 and r2 are drawn, touching the diameter and the semicircle and also touching each other externally. Prove that the maximum value of ( r1+ r2 ) = 2(√2 -1) ...

Prove that the locus of the intersection of AP with the straight line through A' perpendicular to A'P is a straight line which is perpendicular to the major axis of an ellipse. ...

Equation of the common tangent to the parabolas : y^2 = 4ax; x^2 = 4ay ...