List of top Mathematics Questions on Straight lines asked in MHT CET

If the angle made by the lines represented by the equation \(ax^2+2hxy+by^2 = 0\) with X-axis are \(α\) and \(β\), then \(tan(α+β)\) is

A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

If the equation \(16x^2-24xy+9y^2-8x+6y-35 = 0\) represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

The area of a triangle formed by a line with the coordinate axes is \(49\) sq. units. If the perpendicular drawn from the origin to this line makes an angle of \(45^{\circ}\) with the positive X-axis, then the equation of line is....

The family of straight lines \(4ax+3by+c = 0\) such that \(a+b+c = 0\) (where a, b, c are real constants) are concurrent at the point...

If two lines represented by \(x^2-(1+\sqrt{3})xy+\sqrt{3}y^2 = 0\) make angles \(α\) and \(β\) with the X-axis, then \(tan(α+β)\) is...

If the combined equation of angle bisectors of the lines \(x^2-2pxy-y^2 = 0\) is \(x^2-2qxy-y^2 = 0\), then which of the following is true?

A straight line L passes through the point of intersection of the lines \(x-y+1 = 0\) and \(2x+y-7 = 0\). If L intersects the positive x-axis at \(A(a,0)\) and the positive y-axis at \(B(0,b)\), then the minimum area of the triangle \(OAB\) (where \(O\) is the origin) is ....

The coordinates of the orthocenter of the triangle whose sides are represented by the lines \(4x-7y+10 = 0\), \(x+y = 5\) and \(7x+4y = 15\) are \(\ldots\)

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by \(x^2-6xy+5y^2+10x-14y+9 = 0\) is \(\ldots\)

The line \(L_1\) given by \(\frac{x}{p}+\frac{y}{2} = 1\) passes through the point \((5,0)\). The line \(L_2\) given by \(\frac{x}{10}+\frac{y}{q} = 1\) is parallel to \(L_1\). Then the distance between the lines \(L_1\) and \(L_2\) is...

Two lines are given by \(x^2-4xy+4y^2+kx-2ky = 0\), then the value of k so that the distance between them is 3 is

Which of the following statements is/are False?
\(S_1:\exists \,n\in N\), such that \(n^2+n+2\) is divisible by 4.
\(S_2:\exists \,x\in N\), such that \(x-17 < 20\).
\(S_3:\forall \,n\in N,\,x^2+3x-10 = 0\).
\(S_4:\forall \,n\in N,\,n^2\geq 1\).

The negation of \((p∧q)\rightarrow ((p∨r)\rightarrow \,\sim q)\) is equivalent to ...

The measure of the acute angle between the pair of lines \(2x^2+xy-y^2-x+2y-1 = 0\) is:

The joint equation of a pair of lines passing through point \((1,4)\), one of which is parallel to X-axis and the other makes an angle of \(45^{\circ}\) with the positive direction of X-axis, is

If \(A(2,-3)\) and \(C(-6,7)\) are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is

If \(θ\) is the acute angle between the lines \(2x^2+7xy+3y^2 = 0\), then the value of \(\frac{2cosθ-3sinθ}{4sinθ+5cosθ} = \ldots\)

The combined equation of the pair of lines passing through the origin and making an angle \(\frac{π}{4}\) with the line \(3x+y-6 = 0\) is...

The line \((2+k)x+(1+k)y = 5+7k\) passes through the fixed point for different values of k. If 'd' is the distance of a fixed point from the origin, then \(d^2 = \ldots\)

The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)

If \(4ab = 3h^2\), then the ratio of the slopes of the lines represented by \(ax^2+2hxy+by^2 = 0\) is...

The line \(x+y = 3\) intersects the pair of straight lines \(x^2-3xy+y^2 = 0\) at points A and B. Then the co-ordinates of the mid-point of AB are

If a triangle \(ABC\) has vertices \(A(1,-6),B(2,-3)\) and \(C(3,-2)\), then the coordinates of its orthocenter are....

If \(θ\) is the acute angle between the lines represented by the equation \(x^2-3xy+2y^2 = 0\), then \(\frac{3sinθ+2cosθ}{3sinθ-2cosθ} =\)