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

If \(A,B\) are the feet of the perpendiculars drawn from \(P(3,1)\) on the pair of lines \[ 2x^2+3xy-2y^2+3x+y+1=0 \] and \(Q\) is the point of intersection of the pair of lines, then the area of the quadrilateral \(PAQB\) is

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 $g^{2}h^{2}=$

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 $\frac{b+c}{a}=$

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 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:

If one of the roots of the equation \(x^2-5x-14=0\) is the length of the semi-conjugate axis of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and the square of the other root is the semi-transverse axis, then the focus of the hyperbola that lies on the positive \(x\)-axis is

Let \[ E_1=\frac{x^2}{9}+\frac{y^2}{4}=1 \] and \[ E_2=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] be two ellipses and \(R\) be a rectangle with sides parallel to the coordinate axes. Let \(E_1\) be inscribed ellipse in \(R\) and \(E_2\) be circumscribed ellipse on \(R\). If \(E_2\) passes through \((0,4)\), then

The equation of directrix of parabola \(x^2 + 8x + 12y + 4 = 0\) is

Given two points \(Q(3,4)\) and \(R(1,2)\). What is the point \(P(x,y)\) on the line \(2x - y - 1 = 0\) for which \(PQ + PR = QR\) holds?

Suppose the vertices of a triangle are given by \(A(0,3)\), \(B(-2,0)\), and \(C(6,1)\). For \((\alpha, \alpha + 1)\) to lie inside the triangle, \(\alpha\) should lie in the interval

For a triangle formed by \((0,0)\), \((4,0)\), and \((3,4)\), the orthocenter is

Suppose a triangle of area 27 sq. units is formed by \(18x^2 - 9xy + y^2 = 0\) and \(y = c\). Then the centroid of the triangle is