Given `x/a+y/b=1 and ax + by =1` are two variable lines, 'a' and 'b' being the parameters connected by the relation `a^2 + b^2 = ab`. The locus of the point of intersection has the equation
A
`x^(2)+y^(2) +xy - 1 = 0`
B
`x^(2)+y^(2)-xy +1 = 0`
C
`x^(2)+y^(2)+xy +1 =0`
D
`x^(2)+y^(2)-xy - 1=0`
Text Solution
Verified by Experts
The correct Answer is:
A
Let (h,k) be point of intersection then `(h)/(a)+(k)/(b) =1` and `ah +bk = 1` Also it is given that `a^(2)+b^(2) =1` Multiplying (i) and (ii), we get `h^(2) +k^(2) + hk((b)/(a)+(a)/(b)) =1` or `h^(2) +k^(2) +hk = 1` or `x^(2)+y^(2) +xy - 1 = 0`
A variable parabola y^(2) = 4ax, a (where a ne -(1)/(4)) being the parameter, meets the curve y^(2) +x - 2 = 0 at two points. The locus of the point of intersecion of tangents at these points is
For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is
The parameters t and t ' of two points on the parabola y^(2)=4ax ,are connected by the relation t=k^(2)t' .The tangents at their points intersect on the curve :
Two lines are drawn at right angles,one being a tangent to y^(2)=4ax and the other x^(2)=4by Then find the locus of their point of intersection.
The mid point of a variable chord AB of the parabola y^(2)=4ax lies on the line y=px where p is a constant,then find the equation of the locus of the points of intersection of the tangents at A and B.
The straight line x/a+y/b=1 cuts the axes in A and B and a line perpendicular to AB cuts the axes in P and Q. Find the locus of the point of intersection of AQ and BP .
If a pair of variable straight lines x^(2)+4y^(2)+alpha xy=0 (where alpha is a real parameter) cut the ellipse x^(2)+4y^(2)=4 at two points A and B,the locus of the point of intersection of tangents at A and B is
CENGAGE-COORDINATE SYSTEM-Multiple Correct Answers Type
