List of top Mathematics Questions on Coordinate Geometry asked in VITEEE

A straight line through the point \( A(3, 4) \) is such that its intercept between the axes is bisected at \( A \). Its equation is:

The tangent at \( (1, 7) \) to the curve \( x^2 = y - 6 \) touches the circle \( x^2 + y^2 + 16x + 12y + c = 0 \) at:

The equation of the straight line through the intersection of the lines \( x - 2y = 1 \) and \( x + 3y = 2 \) and parallel to \( 3x + 4y = 0 \) is:

The lines \( 2x - 3y - 5 = 0 \) and \( 3x - 4y - 7 = 0 \) are diameters of a circle of area 154 square units, then the equation of the circle is:

If \( (-3, 2) \) lies on the circle \( x^2 + y^2 + 2gx + 2fy + c = 0 \), which is concentric with the circle \( x^2 + y^2 + 6x + 8y - 5 = 0 \), then \( c \) is equal to:

The locus of the mid-points of the focal chord of the parabola \( y^2 = 4ax \) is:

If the axes are shifted to the point \( (1, 2) \) without solution, then the equation \[ 2x^2 + 2y^2 - 4x + 4y = 0 \] becomes:

A line passes through \( (2, 2) \) and is perpendicular to the line \( 3x + y = 3 \). What is its y-intercept?

The number of common tangents to the circles \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 6x - 8y = 24 \) is:

To the lines \( ax^2 + 2hxy + by^2 = 0 \), the line \( ax^2 + 2h(a+b)xy + b^2y^2 = 0 \) are:

The equation \(\lambda x^2+4xy+y^2+\lambda x+3y+2=0\) represents a parabola, if \(\lambda\) is

If two circles \(2x^2+2y^2-3x+6y+k=0\) and \(x^2+y^2-4x+10y+16=0\) cut orthogonally, then the value of \(k\) is

If the equation of an ellipse is \(3x^2+2y^2+6x-8y+5=0\), then which of the following are true?

The equation of the common tangents to the two hyperbolas \(\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\) and \(\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1\), are

The condition that the line \(lx+my=1\) may be normal to the curve \(y^2=4ax\), is

A rod of length \(l\) slides with its ends on two perpendicular lines. Then, the locus of its mid point is

The equation of straight line through the intersection of the lines \(2x+y=1\) and \(3x+2y=5\) and passing through the origin is

The line joining \((5,0)\) to \((10\cos\theta,10\sin\theta)\) is divided internally in the ratio \(2:3\) at \(P\). If \(\theta\) varies, then the locus of \(P\) is

If \(2x+y+k=0\) is a normal to the parabola \(y^2=-8x\), then the value of \(k\) is

The number of normals drawn to the parabola \(y^2=4x\) from the point \((1,0)\) is

If the circle \(x^2+y^2=a^2\) intersects the hyperbola \(xy=c^2\) in four points \((x_1,y_1)\) for \(i=1,2,3,4\), then \(y_1+y_2+y_3+y_4\) equals

The mid point of the chord \(4x-3y=5\) of the hyperbola \(2x^2-3y^2=12\) is

The area (in square unit) of the circle which touches the lines \(4x+3y=15\) and \(4x+3y=5\) is

The area (in square unit) of a triangle formed by \(x+y+1=0\) and the pair of straight lines \(x^2-3xy+2y^2=0\) is

The pairs of straight lines \(x-3y+2y^2=0\) and \(x^2-3xy+2y^2-x-2=0\) form a