Let the equation of line through the point (1,0) having slope m,(m≠0) is y=mx−m, Now, the combined equation of pair of straight lines joining the point of intersections of given curve 2x2+5y2−7x=0 and line y=mx−m to the origin is 2x2+5y2−7x(
mx−y
m
)=0 ⇒2mx2+5my2−7x(mx−y)=0 ⇒−5mx2+5my2+7xy=0.........(i) Since, the Eq. (i) represents the perpendicular lines, because sum of coefficients of x2 terms and y2 terms is zero.