Higher Math 2nd Paper CQ-Chittagong Board-2022

Find the equation of directrix of parabola $x^{2}=$ $-7 y$.

Find the centre, foci and length of latus rectum of ellipse from scenario-1.

Finding the name of the conic from scenario-2, determine the equation of conic.

Find the parametric co-ordinate of the ellipse $\frac{x^{2}}{16}+$ $\frac{y^{2}}{4}=1$ where $\theta$ is an eccentricitic angle.

Find the equation of asymptotes of hyperbola from scenario-1.

Find the equation of hyperbola with the information in scenario-2.

If $a+i b=e^{i \theta}$, then show that, $a^{2}+b^{2}=1$.

Find the cubic root of $z+\bar{z}$ from scenario-1.

From the equation of scenario-2, show that if the roots are real, they will be equal and find the equal roots.

Two forces $4 \mathrm{~N}$ and $8 \mathrm{~N}$ are acting at any point and their resultant is perpendicular to the line of action of $4 \mathrm{~N}$ force. Find the angle between the forces. ?

From scenario-1 prove that, $\tan \frac{\theta}{2}=\frac{F_{1}-F_{2}}{F_{1}+F_{2}} \tan \frac{\alpha}{}$,

From scenario-2 show that, $S=\frac{P_{1}-P_{2}}{P_{1}+P_{2}} A$ $P_{1}>P_{2}$.

Find the modulus and argument of complex number $6-2 \sqrt{3} i$.

Find the locus and indicate its name with diagram of equation indicated in scenario-1.

Show that, $\left(b_{0}-b_{2}+b_{4}-\ldots \ldots . . .\right)^{2}=\left(b_{2}+b_{1}+b_{2}\right.$ $\left.+b_{3}+\ldots . . . ..\right)-\left(b_{1}-b_{3}+b_{5}-\ldots . . . . . .\right)^{2}$ from the equation of scenario-2.