List of top Mathematics Questions on Coordinate Geometry asked in AP EAPCET

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 \(d_1\) and \(d_2\) are the distances of the foci of the hyperbola \(4x^{2}-9y^{2}-16x+54y-101=0\) from the point (2,-3), then \(d_1+d_2=\)

Let \(x+y=0\) be the equation of the latus rectum of a parabola. Let the axis of this parabola pass through the point (1, 1). If \(x+y-2\sqrt{2}=0\) is the equation of the directrix of the parabola, then its vertex is

If the tangent drawn from the point \(P(5,3)\) to the parabola \(y^{2}=x\) is at a distance of \(\frac{1}{\sqrt{5}}\) units from the vertex of the parabola and touches the parabola at the point Q, then \(PQ=\)

X axis is the major axis and origin is the centre of an ellipse. If the distance between its directrices is \(\frac{18}{\sqrt{5}}\) and the ratio between the distances from the centre of this ellipse to its focus and its corresponding directrices is \(5:9\), then the length of its latus rectum is

If the image of \(P(2,3)\) in a line \(L\) is \(Q(4,5)\), find the image of \(R(0,0)\) in the same line \(L\).

The straight line which is parallel to X-axis and passing through the intersection of the lines \( ax+2by+3b=0 \) and \( bx-2ay-3a=0 \), \( (a,b)\neq(0,0) \) is

In \( \triangle ABC \), coordinates of A are (1, 2). If the equations of the medians through B and C are \( x+y=5 \) and \( x=4 \) respectively, then the area of \( \triangle ABC \) (in sq. units) is

If the slope of one of the lines \( 2x^{2}-17xy+by^{2}=0 \) is 16 times the slope of another line, then the angle between this pair of lines is

The square of the distance from the origin to the point of intersection of the pair of lines \( ax^{2}-xy-3y^{2}-5x+20y-25=0 \) is

The product of the lengths of the perpendiculars drawn from the point $(1, 2)$ to the pair of lines $2x^{2}-3xy-2y^{2}=0$ is

If the equation $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ represents a pair of parallel lines, then $g^{2}h^{2}=$

Let $A(1,2)$ and $C(3,4)$ be the end points of one of the diagonals of a square $ABCD$. If $B(\alpha,\beta)$ and $D(\gamma,\delta)$ are the end points of another diagonal of this square, then $\alpha+\beta-\gamma+\delta=$

The equation of a line $L_{1}$ passing through the point $(2, 4)$ and making an angle $\tan^{-1}(2)$ with another line $x+2y=4$ is $ax+by+c=0$. If this line $L_{1}$ is neither horizontal nor vertical, then $\frac{b+c}{a}=$

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is:

For the parabola represented in the parametric form \[ x=t^2+t+1 \] \[ y=t^2-t+1, \] the length of latus rectum is:

The foci of the ellipse \[ 9x^2+25y^2=225 \] are

If \((1,2)\) is the focus, \(x+2y=0\) is the directrix and \(\sqrt{2}\) is the eccentricity of a hyperbola, then the equation of the hyperbola is

The locus of the point of intersection of the lines \[ \sqrt3x-y-4\sqrt3k=0 \] and \[ \sqrt3kx+ky-4\sqrt3=0 \] for different real values of \(k\) is a hyperbola \(H\). If \(e\) is the eccentricity of \(H\), then \(4e^2=\)

If the directrix of the parabola \[ x^2+4y-6x+\lambda=0 \] is \(y+1=0\), then which of the following is correct?

A point \(P(x,y)\) is such that the sum of squares of its distances from \((a,0)\) and \((-a,0)\) is \(2b^2\). The equation representing the locus of \(P\) is:

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

A point \(P\) on a line is at a distance of \(4\) units from the origin \((0,0)\). If the line makes \(60^\circ\) with the negative direction of the \(x\)-axis, then \(P\) is