If `theta` is the acute angle between the lines with slopes m1 and m2 then `tantheta = (m_1 -m_2)/(1+m_1m_2)`. 2) if p is the length the perpendicular from point P(x1, y1) to the line ax+ by +c =0 then p= `(ax_1+by_1+c)/(sqrt(a^2+b^2))`

If theta is the acute angle between the lines with slopes m1 and m2 then tantheta = (m_1 -m_2)/(1+m_1m_2) .If p is the length the perpendicular from point P(x1, y1) to the line ax+ by +c =0 then p= (ax_1+by_1+c)/(sqrt(a^2+b^2))

If theta is the acute angle between the lines with slopes m1 and m2 then tan theta=(m_(1)-m_(2))/(1+m_(1)m_(2)) 2) if p is the length the perpendicular from point P(x1,y1) to the line ax +by+c=0 then p=(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))

State True or False: Acute angle between two lines with slopes m and m_(2) is given by tantheta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|

(i ) If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2)) (ii) If the length of perpendicular from point (1,1) to the line ax-by+c=0 is unity then show that : (1)/(a)-(1)/(b)+(1)/(C )=(c )/(2ab)

prove that the product of the perpendiculars drawn from the point (x_1, y_1) to the pair of straight lines ax^2+2hxy+by^2=0 is |(ax_1^2+2hx_1y_1+by_1^2)/sqrt((a-b)^2+4h^2)|

Derive a formula for the angle between two lines with slope m1 and m2.Hence find the acute angle between the lines sqrt 3x+y=1 and x+sqrt3 y=1 .

Find the angle between the lines l_(1) : y= (2 - sqrt(3) ) ( x +5) and l_(2) : y=(2+ sqrt(3) ) ( x-7) . Thinking Process : If the angle between the lines having the slope m_1 and m_2 is theta then tan theta = | ( m_1 - m_2)/( 1+ m_1 m_2) | . Use this formula to solve the above problem.

Let the tangents to the parabola y^(2)=4ax drawn from point P have slope m_(1) and m_(2) . If m_(1)m_(2)=2 , then the locus of point P is

Let the tangents to the parabola y^(2)=4ax drawn from point P have slope m_(1) and m_(2) . If m_(1)m_(2)=2 , then the locus of point P is