If the lines `L_1a n dL_2` are tangents to `4x^2-4x-24 y+49=0` and are normals for `x^2+y^2=72 ,` then find the slopes of `L_1` and `L_2dot`

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

The combined equation of the lines l_1a n dl_2 is 2x^2+6x y+y^2=0 and that of the lines m_1a n dm_2 is 4x^2+18 x y+y^2=0 . If the angle between l_1 and m_2 is alpha then the angle between l_2a n dm_1 will be

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1/3dot

Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1/3dot

Find the slopes of the tangents to the parabola y^2=8x which are normal to the circle x^2+y^2+6x+8y-24=0.

If the slope of one line is double the slope of another line and the combined equation of the pair of lines is ((x^2)/a)+((2x y)/h)+((y^2)/b)=0 , then find the ratio a b: h^2dot

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

theta_1 and theta_2 are the inclination of lines L_1a n dL_2 with the x-axis. If L_1a n dL_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is (a) (x-x_1)/(cos((theta_1+theta_2)/2))=(y-y_1)/(sin((theta_1+theta_2)/2)) (b) (x-x_1)/(-sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2)) (c) (x-x_1)/(sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2)) (d) (x-x_1)/(-sin((theta_1+theta_2)/2))=(y-y_1)/(cos((theta_1+theta_2)/2))