S L Loney Solutions for Chapter: Conic Sections. The Parabola, Exercise 2: EXAMPLES XXVI

The equations of the tangent and the normal at the point $\left(4, 6\right)$ of the parabola $y^2=9x$ are $cy-3x=d \& 3y+ax=b$, respectively. Find $a+b+c+d$.

The equations of the tangent and the normal at the point of the parabola $y^2=6x$, whose ordinate is $12$ are $4y-ax=b \& y+cx=d$, respectively. Find $a+b+c+d$.

At the ends of the latus rectum of the parabola $y^2=4a\left(x-a\right)$, the equations of tangents are $x+y=pa \& x-y=qa$ and equations of the normals are $x+y=ra \& x-y=sa$, where $p, q, r, s$ are integers. Find $p+q+r+s$.

The equation of that tangent to the parabola $y^2=7x$ which is parallel to the straight line $4y-x+3=0$ is $4y-x=a$ and its point of contact is $\left(b,c\right)$. Find $a-b+c$.

A tangent to the parabola $y^2=4ax$ makes an angle of $60°$ with the axis and its point of contact is $\left(\frac{a}{3},\frac{ka}{\sqrt{3}}\right)$, then find $k$.

A tangent to the parabola $y^2=8x$ makes an angle of $45°$ with the straight line $y=3x+5$. If the equations are $2y+ax+b=0 \& 2y+cx+d=0$ and the points of contact of these tangents are $(p,q) \& \left(r, s\right)$, respectively. Find $abcd+pqrs$.

The points on the parabola $y^2=4ax$ at which $\left(\mathrm{i}\right)$ the tangent and $\left(\mathrm{i}\mathrm{i}\right)$ the normal is inclined at $30°$ to the axis of the parabola are $(3a, 2\sqrt{\beta }a)$ and $(\frac{a}{3},-\frac{2\sqrt{\gamma }}{3}a)$, respectively. Find $\beta +\gamma$.

The equation of the tangents to the parabola $y^2=9x$ which goes through the point $\left(4,\mathrm{}10\right)$ are $4y=px+q \& 4y=rx+s$. Find $p+q+r+s$.