31 Geometry • Conic Sections For what value of c is the line y=0.5x+c tangent to the parabola y^2=4ax? For what value of c is the line y=0.5x+c tangent to the parabola y^2=4ax? सेव करें Save सेव्ड Saved A. a/2 a/2 B. a/4 a/4 C. 2a 2a D. a a उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: C Correct Answer: C A tangent to y^2=4ax with slope m has equation y=mx+a/m. With m=0.5, the intercept is c=a/0.5=2a. A tangent to y^2=4ax with slope m has equation y=mx+a/m. With m=0.5, the intercept is c=a/0.5=2a.
32 Geometry • Conic Sections Which conic does the equation R=5/(4-11cos(omega)) represent? Which conic does the equation R=5/(4-11cos(omega)) represent? सेव करें Save सेव्ड Saved A. Hyperbola Hyperbola B. Parabola Parabola C. Ellipse Ellipse D. Circle Circle उत्तर और व्याख्या देखें Show answer and explanation सही उत्तर: A Correct Answer: A Writing the denominator in standard polar-conic form shows eccentricity e=11/4. Since e>1, the conic is a hyperbola. Writing the denominator in standard polar-conic form shows eccentricity e=11/4. Since e>1, the conic is a hyperbola.