y=4a^(2)x+(a^(4)-b^(4))=0

x-2y+4=0 is a common tangent to y^(2)=4x and (x^(4))/(4)+(y^(2))/(b^(2))=1. Then the value of b and the other common tangent are given by : (A) b=sqrt(3)(B)x+2y+4=0(C)b=3 (D) x-2y-4=0

Match the following. {:("Line, parabola"," "," ""Pole"),("I". 2x-3y+4=0,y^(2)=4x," "(a)(4,6)),("II". 2x+3y-4=0,y^(2)=4x," "(b)(2,3)),("III". x-2y+4=0,y^(2)=6x," "(c)(-2,-3)),("IV". 3x+4y-4=0,x^(2)=4y," "(d)(-3//2,-1)):}

Divide: x^(4a)+x^(2a)y^(2b)+y^(4b)byx^(2a)+x^(a)y^(b)+y^(2b)

Factorize: 4x^(2)+12xy+9y^(2)(ii)x^(4)-10x^(2)y^(2)+25y^(4)a^(4)-2a^(2)b^(2)+b^(4)

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy=c^(2) is (A)(x^(2)-y^(2))^(2)+4c^(2)xy=0(B)(x^(2)+y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4c2^(x)y=0(C)x^(2)-y^(2))^(2)+4cxy=0(D)(x^(2)+y^(2))^(2)+4cxy=0

Equations of the common tangents to the parabola, y=x^(2) and y=-(x-2)^(2) are [x=0,x=4y-2],[x=0,y=4x-2],[y=0,y=4x+4],[y=0,y=4x-4]

Statement 1: The equations of the straight lines joining the origin to the points of intersection of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0 is x-y=0 . Statement 2: y+x=0 is the common chord of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0

If (x)/(y)=(a+2)/(a-2), then (x^(2)-y^(2))/(x^(2)+y^(2)) is equal to (8a)/(a^(2)+4)(b)(4a)/(a^(2)-4)(c)(4)/(a^(2))(d)(4a)/(a^(2)+4)

The solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0 is (a) x^(4)+y^(4)+x^(2)y^(2)=c (b) x^(4)+y^(4)+3x^(2)y^(2)=c (c) x^(4)+y^(4)+6x^(2)y^(2)=c (d) x^(4)+y^(4)+9x^(2)y^(2)=c

Divide: x^(4a)+x^(2a)y^(2b)+y^(4b)\ b y\ \ x^(2a)+\ x^a\ y^b+\ y^(2b)