List of top Mathematics Questions on x-intercepts and y-intercepts

For \(1 \leq x<\infty\), let \(f(x) = \sin^{-1}\left(\frac{1}{x}\right) + \cos^{-1}\left(\frac{1}{x}\right)\). Then \(f'(x) =\)

\[ \int_0^{\frac{\pi}{4}} (\tan^3 x + \tan^5 x) \, dx \]

Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then:

If \[ \sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \frac{3\pi}{2}, \] then \( x + y + z = \):
If a line makes an angle of $\pi/3$ with each of $x$ and and $y$-axis, then the acute angle made by $z$-axis is
If the perpendicular bisector of the line segment joining $A(\alpha, 3)$ and $B (2, -1)$ has $y$-intercept $1$, then $\alpha$ =
Variable straight lines $y = mx + c$ make intercepts on the curve $y^2 - 4ax = 0$ which subtend a right angle at the origin. Then the point of concurrence of these lines $y = mx + c$ is
$A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
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 locus of the orthocentre of the triangle formed by the lines $(1 + p )x -p y + p (1 + p) = 0 (1+ q)x-qy + < 7(1+ q) = 0$ and $y = 0$, where $p\ne q$ is
The locus of the point of intersection of lines $x \cos \, \alpha + y \sin \alpha = a$ and $x \sin \alpha - y \cos \alpha = b$ ($\alpha$ is a variable)
The lines $a_1x + b_1y + c_1 = 0$, $a_2x + b_2y + c_2 - 0$ and $a_3x = 0$ are concurrent, if $b_1c_2 - b_2c_1$ is equal to