the given curve is hyperbola.
for hyperbola x2/a2−y2/b2=1x^2/a^2 - y^2/b^2=1 x2/a2−y2/b2=1
any line y=mx+c is tangent if c2=a2m2−b2c^2= a^2m^2-b^2c2=a2m2−b2 ......(1)
. so now perpendicular to 5x+2y-10=0 means slope of tangent is 2/5
use in 1
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