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The equation of the locus of the point(asecp+btanp,atanp+bsecp)

The equation of the locus of the point(asecp+btanp,atanp+bsecp)

Grade:10

1 Answers

Arun
25763 Points
3 years ago
 
 
 
x = a secp + b tanp
y = a tanp + b secp
 
x² = a² sec²p + b² tan²p + 2ab secp tanp
y² = a² tan²p + b² sec²p + 2ab secp tanp
 
Now
 
x² - y² = a²(sec²p - tan²p) + b²( tan²p - sec²p)
 
x² - y² = a² - b²
 
Hence this will be the equation.
Which reperesere hyperbola.
 
 
 
Regards
Arun (askIITians forum expert)

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