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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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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 \(d_1+d_2=\)
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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 \(PQ=\)
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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 \(L\).
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
If the equation $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ represents a pair of parallel lines, then $g^{2}h^{2}=$
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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 $\alpha+\beta-\gamma+\delta=$
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
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 $\frac{b+c}{a}=$
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
The foot of the perpendicular from the point $(1, 3)$ to the line $x + y - 2 = 0$ is:
AP EAPCET - 2026
AP EAPCET
Mathematics
Coordinate Geometry
For the parabola represented in the parametric form \[ x=t^2+t+1 \] \[ y=t^2-t+1, \]
the length of latus rectum is:
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
The foci of the ellipse \[ 9x^2+25y^2=225 \]
are
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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 \(4e^2=\)
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
If the directrix of the parabola \[ x^2+4y-6x+\lambda=0 \]
is \(y+1=0\), then which of the following is correct?
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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:
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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?
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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
AP EAPCET - 2022
AP EAPCET
Mathematics
Coordinate Geometry
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