List of top Mathematics Questions on Coordinate Geometry asked in LPUNEST

What conic does \(13x^2 - 18xy + 37y^2 + 2x + 14y - 2 = 0\) represent?
The order and degree of the differential equation \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}} = k\left(\frac{d^2y}{dx^2}\right) \] are respectively:
If the points \((1,1)\), \((-1,-1)\) are the vertices of a triangle, then this triangle is:
Find the centre and radius of the circle \(2x^2 + 2y^2 = 3x - 5y + 7\).

The number of integral values of \(\lambda\) for which \(x^2 + y^2\) +\(\lambda\) x + (1 - \(\lambda\))y + 5 = 0 is the equation of a circle whose radius does not exceed 5 is

A line cuts the \(x\)-axis at \(A(7,0)\) and the \(y\)-axis at \(B(0,-5)\). A variable line \(PQ\) is drawn perpendicular to \(AB\) cutting the \(x\)-axis and \(y\)-axis at \(P\) and \(Q\) respectively. If \(AQ\) and \(BP\) intersect at \(R\), then the locus of \(R\) is:
A straight line through the origin \(O\) meets the parallel lines \(4x+2y=9\) and \(2x+y+6=0\) at points \(P\) and \(Q\) respectively. The point \(O\) divides the segment \(PQ\) in the ratio:
The number of values of c such that the straight line \(y=4x+c\) touches the curve \(\frac{x^2}{4}+y^2=1\) is
If \(A=\{(x,y)\mid x^2+y^2\le 4;\; x,y\in \mathbb{R}\}\) and \(B=\{(x,y)\mid x^2+y^2\ge 9;\; x,y\in \mathbb{R}\}\), then
The ratio of the coefficient of $x^{15}$ to the term independent of $x$ in the expansion of $\left(x^2+\dfrac{2}{x}\right)^{15}$ is
Let $f$ be a polynomial function such that $f'(x)=f(x)\,f''(x)$ for all $x\in\mathbb{R}$. Then:
The minimum distance of a point on the curve $y=x^2-4$ from the origin is
Evaluate: \[ \int \frac{dx}{\cos x+\sqrt{3}\sin x} \]