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

The equation of the normal to the curve \(3x^2 + y^2 = 8\), which is parallel to the line \(x + 3y = 10\) is?

If a pair of line given by \( (x \cos \alpha + y \sin \alpha)^2 = (x^2 + y^2) \sin^2 \alpha \) are perpendicular. What is the value of α?

If ax + by + c = 0 is normal to xy = 1, then determine if a and b are less than, greater than, or equal to zero.

If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then

The equation of the perpendicular bisector of the line segment joining $A(-2, 3)$ and $B(6, -5)$ is
Area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is
If the slope of one of the lines $ax^2 + 2hxy + by^2 = 0$ is twice that of the other, then $h^2 : ab$ is
If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of $15^\circ$, then the equation of the line in its new position is
If the sum of slopes of lines represented by $ax^2+8xy+5y^2=0$ is twice their product, then $a =$
The combined equation of a pair of lines passing through the origin and inclined at $60^\circ$ and $30^\circ$ respectively with X-axis is
If two lines represented by $ax^2 + 2hxy + by^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of X-axis, then $\tan(\alpha + \beta) =$
If the slopes of the lines given by the equation $ax^2 + 2hxy + by^2 = 0$ are in the ratio $5 : 3$, then the ratio $h^2 : ab =$
The distance between the parallel lines $3x + 4y = 9$ and $6x + 8y = 15$ is
The joint equation of pair of lines through the origin and having slopes $(1+\sqrt{2})$ and $\frac{1}{(1+\sqrt{2})}$ is
If $4ab = 3h^2$, then the ratio of slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is
If one of the lines given by $kx^2 + xy - y^2 = 0$ bisects the angle between the co-ordinate axes, then the values of $k$ are
If the lines represented by $ax^2 - bxy - y^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis, then $\tan(\alpha + \beta) = $
If the lines $x^2 - 4xy + y^2 = 0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis, then $\cot^2\alpha + \cot^2\beta =$
If $p$ is the length of the perpendicular from origin to the line whose intercepts on the axes are $a$ and $b$, then $\frac{1}{a^2} + \frac{1}{b^2} =$
If $(\text{m}+3\text{n})(3\text{m}+\text{n})=4\text{h}^2$, then the acute angle between the lines represented by $\text{m} \text{x}^2+2\text{h}\text{xy}+\text{n}\text{y}^2=0$ is
The joint equation of pair of lines through the origin and making an equilateral triangle with the line $y=3$ is
If the equation $3x^2 - kxy - 3y^2 = 0$ represents the bisectors of angles between the lines $x^2 - 3xy - 4y^2 = 0$, then value of $k$ is
If the two lines given by $ax^2 + 2hxy + by^2 = 0$ make inclinations $\alpha$ and $\beta$, then $\tan(\alpha + \beta) =$
The joint equation of two lines through the origin, each of which makes an angle of \(30^\circ\) with the line \(x + y = 0\), is
If one of the lines given by \( kx^2 + xy - y^2 = 0 \) bisects the angle between the co-ordinate axes, then values of \( k \) are: