List of top Mathematics Questions on Coordinate Geometry

There is a triangular park in the society. The park is divided into two sections as shown in the figure. The vertices of the triangular park ABC are A(0, 4), B(\(-2\), 0) and C(3, 0). Based on the above information, answer the following questions :

The value of p such that the line joining (0,3), (5, -2) is a tangent to the curve $y = \frac{p}{x+1}$ is

The equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola if}

The vertex of the parabola $y=ax^2+bx+c$ is

The equation of major axis of the ellipse $\frac{(x-1)^2}{9}+\frac{(y-6)^2}{4}=1$ is

If the line $3x-2y+6=0$ meets x-axis and y-axis respectively at A and B, then the equation of the circle with radius AB and centre at A is

The largest distance from (-3, 2) to the circle $x^{2} + y^{2} - 2x + 2y + 1 = 0$

The equation $16x^2+y^2+8xy-74x-78y+212=0$ represents

Let P be a variable point such that it forms a triangle of area 14 square units with two fixed points \((-3,4)\) and \((4,-3)\). Then the locus of P represents a pair of parallel lines. The distance between these two parallel lines is

Let P be any point on circle \(x^2+y^2=16\) and \(A=(1,2)\). If the locus of point dividing AP in ratio 3:2 is a circle, its radius is:

If a circle inscribed in the parabola \(y^{2}=4ax\) passes through its focus, then the equation of the circle is:

If line \(4x-3y+c=0\) makes a chord of length 10 on circle \(x^2+y^2-2x+4y-23=0\), then \(c=\):

If \(3x+4y-24=0\) and \(3x-4y-32=0\) are tangents to a circle and \(4x+3y-1=0\) is a normal, then \(r+h+k=\):

The tangent drawn at a point \(P\) on the circle \(x^{2}+y^{2}+6x+6y-2=0\) cuts the line \(5x-2y+6=0\) at a point \(Q\). If \(PQ=5\), then a point \(Q\) having integral coordinates is:

If two vertices of a quadrilateral are the centres of the circles \[ S\equiv x^{2}+y^{2}-2x-2y-2=0 \] and \[ S^{\prime}\equiv x^{2}+y^{2}-6x-6y+14=0 \] and the other two vertices of that quadrilateral are the points of intersection of these two circles, then the area of the quadrilateral is:

A ray from (7,2) reflects on \(2x+y=1\) and passes through (3,10). Equation of incident ray is:

The line \((3a+1)x+(7a+2)y=17a+5\) represents concurrent lines. If \(d\) is distance from \((3,1)\) to line of slope 1 in this family, find \(2d^2\):

In triangle ABC, B lies on positive x-axis, A=(-1,0), \(a=4\sqrt{3}\), \(\angle A=120^\circ\). If C has integer coordinate condition, distance of C from origin is:

If the coordinate axes are rotated about the origin through \(60^\circ\), the equation \(x^{2}+y^{2}-4x-8y+16=0\) becomes \(x^{2}+y^{2}+2Gx+2Fy+C=0\). Then \(G+F+C=\):

One of the pair of lines \(x^{2}-3y^{2}-4x-6\sqrt{3}y-5=0\) is \(x+by+c=0\) \((b<0)\). If the other line intersects the curve \(x^{2}-5y^{2}-4x=0\) at two points A and B, then \(\angle AOB=\):

The circumcenter of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points \((a^2+1,a^2+1)\) and \((2a,-2a)\), where \(a\neq0\). Then the equation of the parabola passing through the orthocentre is

If \(O\) is the origin and \(P\) is a point moving on the straight line \(lx + my + n = 0 \; (n \neq 0)\). If \(Q\) is a point on the segment \(OP\) such that \(OP \cdot OQ = k^2\), where \(k \neq 0\), then the locus of \(Q\) is

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

The distance between the internal and external centres of similitude with respect to the circles \[ x^2+y^2+4x+6y+12=0 \] and \[ x^2+y^2-6x-4y+9=0 \] is:

If the circles \[ x^2+y^2+2gx+6y+4=0 \] and \[ x^2+y^2-gx-2y-14=0 \] cut each other orthogonally for a positive integral value of \(g\), then the radical axis of the two circles is: