Straight lines `y=m x+c_1` and `y=m x+c_2` where `m in R^+,` meet the x-axis at `A_1a n dA_2,` respectively, and the y-axis at `B_1a n dB_2,` respectively. It is given that points `A_1,A_2,B_1,` and `B_2` are concylic. Find the locus of the intersection of lines `A_1B_2` and `A_2B_1` .

If the tangent and the normal to x^2-y^2=4 at a point cut off intercepts a_1,a_2 on the x-axis respectively & b_1,b_2 on the y-axis respectively. Then the value of a_1a_2+b_1b_2 is equal to:

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

A straight line through the point (1,1) meets the X-axis at A and Y-axis at B. The locus of the mid-point of AB is

If the tangent and normal to the hyperbola x^(2) - y^(2) = 4 at a point cut off intercepts a_(1) and a^(2) respectively on the x-axis, and b_(1) and b_(2) respectively on the y-axis, then the value of a_(1)a_(2) + b_(1)b_(2) is

A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to the parabola at Aa n dB meet the y-axis at A_1a n dB_1 , respectively. If the area of trapezium AA_1B_1B is equal to 12 a^2, then the angle subtended by A_1B_1 at the focus of the parabola is equal to 2tan^(-1)(3) (b) tan^(-1)(3) 2tan^(-1)(2) (d) tan^(-1)(2)

A line x+3y=12 cuts the xa n dy axis in Aa n dB respectively. If Pa n dQ being the points of trisection of A B(P being closer to A) and m_1,m_2 are the slope of the lines O P and O Q respectively (' O ' is the origin), then m_2=2m_1 (b) m_2=3m_1 m_2=4m_1 (d) m_2=5m_1

If a line with direction ratios (1,1,2) intersects the lines x=y+b=z and x+b=2y=z then the coordinates of the points of intersection respectively are given by