Class 11

Math

Co-ordinate Geometry

Straight Lines

The figure is given

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Find the coordinates of the foot of perpendicular from the point $(1,3)$to the line $3x4y16=0$.

Find the distance between $P(x_{1},y_{1})$and $Q(x_{2},y_{2})$when: (i) $PQ$is parallel to the yaxis, (ii) PQ is parallel to the xaxis.

If one of the lines of the pair $ax_{2}+2hxy+by_{2}=0$ bisects the angle between the positive direction of the axes. Then find the relation for $a,b,andh˙$

The two lines represented by $3ax_{2}+5xy+(a_{2}−2)y_{2}=0$ are perpendicular to each other for (a) two values of $a$ (b) a (c) for one value of $a$ (d) for no values of $a$

Show that the pairs of straight lines $2x_{2}+6xy+y_{2}=0$ and $4x_{2}+18xy+y_{2}=0$ have the same set of angular bisector.

The vertices of $Δ$ PQR are $P(2,1)$, $Q(2,3)$and $R(4,5)$. Find equation of the median through the vertex R.

$x+y=7$ and $ax_{2}+2hxy+ay_{2}=0,(a=0)$ , are three real distinct lines forming a triangle. Then the triangle is (a) isosceles (b) scalene equilateral (d) right angled

Reduce the following equations into intercept form and find their intercepts on the axes.(i) $3x+2y12=0$, (ii) $4x3y=6$, (iii) $3y+2=0$.