Hyperbola question.

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Is it possible to solve the question in least amount of steps? My attempt: I first formed the equation of the normal and then I found out the points where it cuts the conjugate and transverse axis. After finding these points I used distance formula to find the distance required and convert it in the form that the question asked. But its a long method and took lot of stepsenter image description here I asked the same question last time but got no response..